From meyer@imap.theory.csail.mit.edu Mon Nov 28 14:37:57 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jASJbv5o004382 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 14:37:57 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jASJbtDC025710 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 14:37:55 -0500 (EST) Received: from PRAVEENPAMIDI.mit.edu (KS-ONE-FIFTY-TWO.MIT.EDU [18.235.1.152]) (authenticated bits=0) (User authenticated as mukkala@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jASJbqba027382 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 14:37:53 -0500 (EST) Message-Id: <6.2.1.2.2.20051128140633.03e5fa00@po12.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.1.2 Date: Mon, 28 Nov 2005 14:38:02 -0500 To: 6042-probs@theory.csail.mit.edu From: Praveen Pamidimukkala Subject: [Sayan] Week 12 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO Content-Length: 355 X-IMAPbase: 1126748715 1136 NonJunk $Label4 $Label1 $Label2 $Label3 $Label5 Junk $MDNSent $Forwarded NotJunk X-UID: 1046 X-Status: A X-Keywords: NotJunk In section 4.3 of the Course Notes on Probability, disjointness is mentioned in comparison to independence. I understand that mathematically, when two events are disjoint, Pr{AintB} = 0 as opposed to Pr{AintB} = Pr{A} x Pr{B}, which applies for independence. However, in terms of events, how could this be described? Thanks, Praveen Pamidimukkala From meyer@imap.theory.csail.mit.edu Mon Nov 28 18:12:32 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jASNCW5o003459 for <6042-probs@theory.lcs.mit.edu>; Mon, 28 Nov 2005 18:12:32 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jASNCV3o018516 for <6042-probs@theory.lcs.mit.edu>; Mon, 28 Nov 2005 18:12:31 -0500 (EST) Received: from hzhou.mit.edu (BURTON-SIX-TWENTY-FOUR.MIT.EDU [18.247.7.113]) (authenticated bits=0) (User authenticated as hzhou@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jASNCCpc009185 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Mon, 28 Nov 2005 18:12:24 -0500 (EST) Message-Id: <5.2.1.1.2.20051128181100.02b043b8@po9.mit.edu> X-Sender: hzhou@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Mon, 28 Nov 2005 18:12:15 -0500 To: 6042-probs@theory.lcs.mit.edu From: Steven Zhou Subject: David-tp13 reading comment Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO Content-Length: 144 X-UID: 1047 X-Keywords: NonJunk NotJunk Hey, Reading and lecture were clear. I found the ability to get a percentage confidence for sampling data to be interesting. - Steven Zhou From meyer@imap.theory.csail.mit.edu Mon Nov 28 19:19:41 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT0Jf5o021596 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 19:19:41 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT0Je3o003544 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 19:19:40 -0500 (EST) Received: from w92-130-webmail-5.mit.edu (W92-130-WEBMAIL-5.MIT.EDU [18.7.22.136]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT0JbOW024603 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 19:19:38 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-5.mit.edu (8.12.4) id jAT0Jb5R027958; Mon, 28 Nov 2005 19:19:37 -0500 Received: from ab6.draper.com (ab6.draper.com [192.80.95.243]) (User authenticated as icharny@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Mon, 28 Nov 2005 19:19:37 -0500 Message-ID: <20051128191937.pl45v83e6tdwgcgk@webmail.mit.edu> Date: Mon, 28 Nov 2005 19:19:37 -0500 From: Isaac Charny To: 6042-probs@theory.csail.MIT.EDU Subject: [Sayan] Week 13 Comments MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO Content-Length: 121 X-UID: 1048 X-Keywords: NonJunk NotJunk I don't understand binomial distribution (section 3.4, page 11). Please discuss this in the next lecture. ~Isaac Charny From meyer@imap.theory.csail.mit.edu Mon Nov 28 19:51:40 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT0pe5o001999 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 19:51:40 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT0pJ3o023281 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 19:51:20 -0500 (EST) Received: from [18.234.1.61] (DP-SIXTY-ONE.MIT.EDU [18.234.1.61]) (authenticated bits=0) (User authenticated as a_lopez@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT0pCVM001023 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 19:51:13 -0500 (EST) Message-ID: <438BA605.10505@mit.edu> Date: Mon, 28 Nov 2005 19:51:17 -0500 From: Adriana Lopez User-Agent: Mozilla Thunderbird 1.0 (Windows/20041206) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.csail.mit.edu Subject: [Jelani] week 13 reading Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-Status: A Content-Length: 612 X-UID: 1049 X-Keywords: NonJunk NotJunk The section on polling was very confusing, I haven't quite understood it yet. I would like this to be explained better in class. There are a lot of variables and equations and it's hard to follow. I forgot what the goal of all this was by the fourth paragraph, and had to reread it a couple of times to understand why each equation brought us closer to what we wanted. Also, in the tutor problems, there was a question that included the concept of variance, but this was not mentioned in the notes (or at least I couldn't find it). This made it a lot more difficult to solve the problem. Adriana From meyer@imap.theory.csail.mit.edu Mon Nov 28 22:02:53 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT32r5o029585 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 22:02:53 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT32paG014663 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 22:02:52 -0500 (EST) Received: from w20-575-41.mit.edu (W20-575-41.MIT.EDU [18.187.0.60]) (authenticated bits=56) (User authenticated as cwong08@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT32jfL028697 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 22:02:46 -0500 (EST) Received: (from cwong08@localhost) by w20-575-41.mit.edu (8.12.9) id jAT32jO5021918; Mon, 28 Nov 2005 22:02:45 -0500 Subject: [Sayan] Week 13 Comments From: Christopher Wong To: 6042-probs@theory.csail.MIT.EDU Content-Type: text/plain Content-Transfer-Encoding: 7bit Date: Mon, 28 Nov 2005 22:02:45 -0500 Message-Id: <1133233365.21884.1.camel@w20-575-41.mit.edu> Mime-Version: 1.0 X-Mailer: Evolution 2.0.4 X-Spam-Score: 3.816 X-Spam-Level: *** (3.816) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO Content-Length: 74 X-UID: 1050 X-Keywords: NotJunk I would like the approximation methods of page 13 explained more clearly. From meyer@imap.theory.csail.mit.edu Mon Nov 28 23:02:17 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT42H5o025524 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 23:02:17 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT3wFdI021982 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 23:02:16 -0500 (EST) Received: from ajshafer (AJSHAFER.MIT.EDU [18.247.4.109]) (authenticated bits=0) (User authenticated as ajshafer@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT3vw9K014618 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 22:57:58 -0500 (EST) Message-ID: <000201c5f499$15955910$6d04f712@ajshafer> From: "Andrew Shafer" To: <6042-probs@theory.csail.mit.edu> Subject: [Sayan] Week 13 Comments Date: Mon, 28 Nov 2005 22:57:56 -0500 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 X-Spam-Score: -1.215 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO Content-Length: 336 X-UID: 1051 X-Keywords: NonJunk NotJunk Will we be going over those horrible equations for confidence in class? They are still pretty confusing even in the notes. Thanks, Andrew ---------------------------- Illegitmitatum Non Carborundum Est Andrew Shafer, MIT Blog http://shaferandrew.blogspot.com Si hoc legere scis numium eruditionis habes. ---------------------------- From meyer@imap.theory.csail.mit.edu Tue Nov 29 01:01:10 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT61A5o018236 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 01:01:10 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT618bP004349 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 01:01:09 -0500 (EST) Received: from christope8f0c6 (MACGREGOR-ONE-TWENTY-FOUR.MIT.EDU [18.239.5.124]) (authenticated bits=0) (User authenticated as yangc@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT6151v008182 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 01:01:06 -0500 (EST) Message-Id: <200511290601.jAT6151v008182@outgoing.mit.edu> From: "Chris Yang" To: <6042-probs@theory.csail.mit.edu> Subject: [David] Week 13 Comments Date: Tue, 29 Nov 2005 01:03:06 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_002F_01C5F480.A8A39050" X-Mailer: Microsoft Office Outlook, Build 11.0.5510 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcX0qpELJrydoAhpS0me67xMhEI4gg== X-Spam-Score: 0.179 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO Content-Length: 2330 X-UID: 1052 X-Keywords: NonJunk NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_002F_01C5F480.A8A39050 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable For the derivation of the confidence interval stuff, why can we assume p = =3D =BD to continue the calculations for delta? Is it because delta is like the upper bound on the error, and not the error itself? =20 Thanks, Chris Yang=20 ------=_NextPart_000_002F_01C5F480.A8A39050 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

For the derivation of the confidence interval stuff, = why can we assume p =3D =BD to continue the calculations for delta?=A0 Is it = because delta is like the upper bound on the error, and not the error = itself?

 

Thanks,

Chris Yang

------=_NextPart_000_002F_01C5F480.A8A39050-- From meyer@imap.theory.csail.mit.edu Tue Nov 29 01:47:52 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT6lq5o026081 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 01:47:52 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAT6lp8B027797 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 01:47:51 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT6lpi4026773 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 01:47:51 -0500 (EST) Received: from [18.241.6.6] (NEW-TWO-SIXTY-ONE.MIT.EDU [18.241.6.6]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAT6lhok023583 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 01:47:44 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: <59496C9D-DE34-4E43-9C8F-AFB9E97D5BD5@mit.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Hamidou Soumare Subject: {Sayan} Weekly Email Comment Date: Tue, 29 Nov 2005 01:57:19 -0500 X-Mailer: Apple Mail (2.746.2) X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO Content-Length: 205 X-UID: 1053 X-Keywords: NonJunk NotJunk Hi, I didnt quite understand the section on polling and would like to have it gone over in class in more detail, especially the part about the confidence interval and its derivation. Thanks. Hamidou From meyer@imap.theory.csail.mit.edu Tue Nov 29 02:19:04 2005 Message-ID: <438C00E8.1040103@csail.mit.edu> Date: Tue, 29 Nov 2005 02:19:04 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Adriana Lopez CC: 6042-probs@theory.csail.mit.edu Subject: Re: [Jelani] week 13 reading References: <438BA605.10505@mit.edu> In-Reply-To: <438BA605.10505@mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 808 X-UID: 1054 X-Keywords: Variance crept in by accident; will be covered next week. I've revised the tutor problem to indicate this. Thanks for pointing this out. regards, A. Adriana Lopez wrote: > The section on polling was very confusing, I haven't quite understood > it yet. I would like this to be explained better in class. There are > a lot of variables and equations and it's hard to follow. I forgot > what the goal of all this was by the fourth paragraph, and had to > reread it a couple of times to understand why each equation brought us > closer to what we wanted. > Also, in the tutor problems, there was a question that included the > concept of variance, but this was not mentioned in the notes (or at > least I couldn't find it). This made it a lot more difficult to solve > the problem. > Adriana From meyer@imap.theory.csail.mit.edu Tue Nov 29 02:28:27 2005 Message-ID: <438C031A.4040302@csail.mit.edu> Date: Tue, 29 Nov 2005 02:28:26 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Praveen Pamidimukkala CC: 6042-probs@theory.csail.mit.edu Subject: Re: [Sayan] Week 12 Comments References: <6.2.1.2.2.20051128140633.03e5fa00@po12.mit.edu> In-Reply-To: <6.2.1.2.2.20051128140633.03e5fa00@po12.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 640 Status: RO X-UID: 1055 X-Keywords: Are you asking what independent events "look like"? Best answer I can give to that is the picture in section 4.3. By the way, happy to have you reviewing Notes 12, but this week's email is supposed to be about Notes 13. regards, A. Praveen Pamidimukkala wrote: > In section 4.3 of the Course Notes on Probability, disjointness is > mentioned in comparison to independence. I understand that > mathematically, when two events are disjoint, Pr{AintB} = 0 as opposed > to Pr{AintB} = Pr{A} x Pr{B}, which applies for independence. > However, in terms of events, how could this be described? > > Thanks, > Praveen Pamidimukkala > From ksindi@MIT.EDU Tue Nov 29 02:36:40 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT7ae5o008229 for <6042-probs@theory.csail.MIT.EDU>; Tue, 29 Nov 2005 02:36:40 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT7adnA015227 for <6042-probs@theory.csail.MIT.EDU>; Tue, 29 Nov 2005 02:36:39 -0500 (EST) Received: from w92-130-webmail-2.mit.edu (W92-130-WEBMAIL-2.MIT.EDU [18.7.22.132]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT7aVID017167 for <6042-probs@theory.csail.MIT.EDU>; Tue, 29 Nov 2005 02:36:31 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jAT7aV14015847; Tue, 29 Nov 2005 02:36:31 -0500 Received: from c-24-218-110-155.hsd1.ma.comcast.net (c-24-218-110-155.hsd1.ma.comcast.net [24.218.110.155]) (User authenticated as ksindi@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 29 Nov 2005 02:36:31 -0500 Message-ID: <20051129023631.1lr183qjbe4ogwwo@webmail.mit.edu> Date: Tue, 29 Nov 2005 02:36:31 -0500 From: Kamil Y Sindi To: 6042-probs@theory.csail.MIT.EDU Subject: [DAVID] Week 13 Comments MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1057 Content-Length: 208 X-Keywords: NonJunk NotJunk I didn't like the binomial sampling part. Maybe we could list the assumptions on it made in class. I also still don't understand what confidence levels are. I found the random varaibles bit to be very clear. From meyer@imap.theory.csail.mit.edu Tue Nov 29 01:17:29 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT6HR5o019547 for <6042-staff@theory.csail.mit.edu>; Tue, 29 Nov 2005 01:17:27 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAT6HQ8B014631 for <6042-staff@theory.csail.mit.edu>; Tue, 29 Nov 2005 01:17:27 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT6HQKk026034; Tue, 29 Nov 2005 01:17:26 -0500 (EST) Received: from [192.168.1.3] (c-65-96-190-64.hsd1.ma.comcast.net [65.96.190.64]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAT6HNok022508; Tue, 29 Nov 2005 01:17:23 -0500 (EST) Message-ID: <438BF263.4060305@mit.edu> Date: Tue, 29 Nov 2005 01:17:07 -0500 From: David Shin User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Kevin Wang CC: 6042-staff@theory.csail.mit.edu Subject: Re: TP 13.4 typo References: <6.2.3.4.2.20051128235648.029d64e0@po10.mit.edu> In-Reply-To: <6.2.3.4.2.20051128235648.029d64e0@po10.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 3.263 X-Scanned-By: MIMEDefang 2.42 X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on theory.csail.mit.edu X-Spam-Level: X-Spam-Status: No, hits=-4.8 required=3.7 tests=AWL,BAYES_00,RCVD_IN_SORBS autolearn=no version=2.63 Status: RO Content-Length: 411 X-UID: 1058 X-Keywords: NotJunk Indeed, you are correct. Thanks for catching this. The TP has been adjusted accordingly. Let me know if you need to redo this problem. DS Kevin Wang wrote: > Hi, > > I think 8. has a typo: "The probability that the second voter chosen > will favor Gore, given that the *first *voter chosen is from the same > state as the first, may not equal /p/." > > It should be *second* right? > > Thanks, > Kevin From lye@MIT.EDU Tue Nov 29 11:25:25 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jATGPP5o011894 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 11:25:25 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jATGPNWJ018113 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 11:25:24 -0500 (EST) Received: from m66-080-5.mit.edu (M66-080-5.MIT.EDU [18.63.1.5]) (authenticated bits=56) (User authenticated as lye@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jATGPG5m027736 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 11:25:17 -0500 (EST) Received: (from lye@localhost) by m66-080-5.mit.edu (8.12.9) id jATGPGbh018478; Tue, 29 Nov 2005 11:25:16 -0500 (EST) Subject: [Sayan] Week 13 Comments From: Linda Ye To: 6042-probs@theory.lcs.MIT.EDU Content-Type: text/plain Content-Transfer-Encoding: 7bit Date: Tue, 29 Nov 2005 11:25:16 -0500 Message-Id: <1133281516.18412.1.camel@m66-080-5.mit.edu> Mime-Version: 1.0 X-Mailer: Evolution 2.0.4 X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1059 Content-Length: 188 X-Keywords: NonJunk NotJunk 3.3 The Numbers Game This was especially counterintuitive, and thus difficult. It seems strange that by guessing (assuming information you do not know), you would improve your chances. From pgroudas@MIT.EDU Tue Nov 29 16:11:34 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jATLBY5o000517 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 16:11:34 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jATLBWaX014976 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 16:11:32 -0500 (EST) Received: from w92-130-webmail-2.mit.edu (W92-130-WEBMAIL-2.MIT.EDU [18.7.22.132]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jATLBUHU013533 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 16:11:30 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jATLBUYH032127; Tue, 29 Nov 2005 16:11:30 -0500 Received: from 18.233.0.185 ([18.233.0.185]) (User authenticated as pgroudas@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 29 Nov 2005 16:11:30 -0500 Message-ID: <20051129161130.qlhdifxhqzi84c00@webmail.mit.edu> Date: Tue, 29 Nov 2005 16:11:30 -0500 From: Paul Groudas To: 6042-probs@theory.lcs.MIT.EDU Subject: [HANSON] Week 13 reading comments MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1060 Content-Length: 252 X-Keywords: NotJunk I found it difficult to really absorb everything past page 14, it just seemed that once it got to polling it started throwing so much math around that it was too much to get all at once. Hopefully this will all get cleared up in class. -Paul Groudas From nedzel@MIT.EDU Tue Nov 29 18:44:29 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jATNiT5o021409 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 18:44:29 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jATNiRRS017010 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 18:44:28 -0500 (EST) Received: from [18.96.7.69] (SIMMONS-FIVE-EIGHTY.MIT.EDU [18.96.7.69]) (authenticated bits=0) (User authenticated as nedzel@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jATNiMlw007551 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 18:44:26 -0500 (EST) Message-ID: <438CE7F6.8000506@mit.edu> Date: Tue, 29 Nov 2005 18:44:54 -0500 From: "David A. Nedzel" User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [Sayan] Week 13 Comments Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 3.076 X-Spam-Level: *** (3.076) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1061 Content-Length: 195 X-Keywords: NonJunk NotJunk I'm fairly comfortable with this material, I've seen most of it in 6.041. It might be nice to have a refresher during lecture on the expectation & variance of different distributions. - David From brevzin@MIT.EDU Tue Nov 29 20:13:57 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU1Dv5o002952 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 20:13:57 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU1Dtr1020223 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 20:13:56 -0500 (EST) Received: from BARRY.mit.edu (PLP-TWELVE.MIT.EDU [18.218.1.12]) (authenticated bits=0) (User authenticated as brevzin@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU1DmIs028650 (version=TLSv1/SSLv3 cipher=DES-CBC3-SHA bits=168 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 20:13:49 -0500 (EST) Message-Id: <6.1.2.0.1.20051129201038.019f4980@po14.mit.edu> X-Sender: brevzin@hesiod X-Mailer: QUALCOMM Windows Eudora Version 6.1.2.0 Date: Tue, 29 Nov 2005 20:13:52 -0500 To: 6042-probs@theory.csail.mit.edu From: Barry Revzin Subject: [Hanson] Reading Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 3.816 X-Spam-Level: *** (3.816) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1062 Content-Length: 446 X-Status: A X-Keywords: NotJunk You guys go over a lot of definitions for expectation, but what about the more general one ? Let f: X --> R+ be a random variable, the expection is integral over X of f du, where u (mu) is the measure. Also, this entire section will be extremely weird since in 18.103 (Fourier Analysis, Measure Theory) we learn the measure theory side which has its own explanations and descriptions... and symbols. The overlap will be confusing. Barry From mwangi@MIT.EDU Tue Nov 29 20:26:12 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU1QC5o007957 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 20:26:12 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU1QAr1029479; Tue, 29 Nov 2005 20:26:10 -0500 (EST) Received: from IBM-1E80C73FC15.mit.edu (NEW-THREE-NINETY-NINE.MIT.EDU [18.241.6.144]) (authenticated bits=0) (User authenticated as mwangi@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU1Q8pK002305 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT); Tue, 29 Nov 2005 20:26:09 -0500 (EST) Message-Id: <6.2.1.2.2.20051129201602.03ecde20@po12.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.1.2 Date: Tue, 29 Nov 2005 20:26:06 -0500 To: 6042-probs@theory.lcs.mit.edu From: Timothy Mwangi Subject: [Sayan] Week 13 Comments Cc: mitras@MIT.EDU Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1063 Content-Length: 291 X-Keywords: NonJunk NotJunk Passage: 2 The Birthday Principle Page: 4 I found this passage most surprising because of the large probability of two people in a room with n people having the same birthday given that there are d days in a year. It seemed very counter-intuitive. Sincerely, Timothy M. Mwangi From bens@MIT.EDU Tue Nov 29 21:02:44 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU22i5o021065 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 21:02:44 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU22gr1023196 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 21:02:43 -0500 (EST) Received: from [18.221.0.117] ([18.221.0.117]) (authenticated bits=0) (User authenticated as bens@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU22aGc010316 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 21:02:36 -0500 (EST) Message-ID: <438D0827.6070508@mit.edu> Date: Tue, 29 Nov 2005 21:02:15 -0500 From: "Benjamin M. Schwartz" User-Agent: Mozilla Thunderbird 1.0.7 (X11/20051014) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [Jelani] Reading notes Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1064 Content-Length: 211 X-Keywords: NotJunk This number-picking game is very cool. I'm surprised that the best strategy isn't just guess that the numbers span 50. I guess it has to do with the envelope-giver guessing your strategy and working around it. From jehan@MIT.EDU Tue Nov 29 21:11:01 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU2B15o021547 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 21:11:01 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU2B0r1027936 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 21:11:00 -0500 (EST) Received: from mopspeak.mit.edu (EASTCAMPUS-SIX-SIXTY-SEVEN.MIT.EDU [18.238.5.156]) (authenticated bits=0) (User authenticated as jehan@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU2Ar6B011984 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 21:10:54 -0500 (EST) Message-Id: <5.2.1.1.2.20051129210818.00bc2650@po14.mit.edu> X-Sender: jehan@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Tue, 29 Nov 2005 21:13:03 -0500 To: 6042-probs@theory.csail.mit.edu From: Jehan deFonseka Subject: [Sayan] Week 13 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1065 Content-Length: 79 X-Keywords: NonJunk NotJunk I thought the mean time to failure thing was pretty cool. no questions jehan From aston@MIT.EDU Tue Nov 29 22:02:29 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU32T5o005619 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 22:02:29 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU32Sr1029851 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 22:02:28 -0500 (EST) Received: from astonlaptop (NEW-THREE-TWENTY-SIX.MIT.EDU [18.241.6.71]) (authenticated bits=0) (User authenticated as aston@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU32K8s022590 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 22:02:21 -0500 (EST) Message-Id: <200511300302.jAU32K8s022590@outgoing.mit.edu> From: "Aston Motes" To: <6042-probs@theory.csail.mit.edu> Subject: [Hanson] Week 13 Comments Date: Tue, 29 Nov 2005 22:02:18 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0006_01C5F530.914B1760" X-Mailer: Microsoft Office Outlook, Build 11.0.6353 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcX1WnmLayKZxAc1QOO1hsICJQY7mg== X-Spam-Score: 2.779 X-Spam-Level: ** (2.779) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1066 Content-Length: 2343 X-Keywords: NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_0006_01C5F530.914B1760 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Pages 12 and 13 mention a closed form formula for the binomial density function approximation, but I was extremely confused by the lack of rationalization for elements in the formula. I suppose we can take it on faith, but I feel kind of uncomfortable about that. - Aston ------=_NextPart_000_0006_01C5F530.914B1760 Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: quoted-printable

Pages 12 and 13 mention a closed form formula for the binomial density function approximation, but I was extremely confused by = the lack of rationalization for elements in the formula. I suppose we can = take it on faith, but I feel kind of uncomfortable about = that.

 

         =    - Aston

------=_NextPart_000_0006_01C5F530.914B1760-- From hectorb@MIT.EDU Tue Nov 29 22:05:01 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU3515o005885 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 22:05:01 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU34wr1001488; Tue, 29 Nov 2005 22:04:58 -0500 (EST) Received: from [18.246.7.127] (BEXLEY-SIX-THIRTY-EIGHT.MIT.EDU [18.246.7.127]) (authenticated bits=0) (User authenticated as hectorb@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU34orn023086 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT); Tue, 29 Nov 2005 22:04:50 -0500 (EST) Message-ID: <438D16D1.7020506@mit.edu> Date: Tue, 29 Nov 2005 22:04:49 -0500 From: Hector Beltran User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.csail.mit.edu Subject: [Hanson] Week 13 Comments Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1067 Content-Length: 400 X-Keywords: NonJunk NotJunk 5.1 Equivalent Definitions of Expectation "There are some other ways of writing the definition of expectation. Sometimes using one of these other formulations can make computing an expectation a lot easier. One option is to group together all outcomes on which the random variable takes on the same value." p. 18-19 This section was not so clear and I would like to see it explained in lecture. From meyer@imap.theory.csail.mit.edu Tue Nov 29 22:17:32 2005 Message-ID: <438D19D2.2000502@csail.mit.edu> Date: Tue, 29 Nov 2005 22:17:38 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Barry Revzin Subject: Re: [Hanson] Reading References: <6.1.2.0.1.20051129201038.019f4980@po14.mit.edu> In-Reply-To: <6.1.2.0.1.20051129201038.019f4980@po14.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 1008 X-UID: 1068 X-Keywords: 18.103 is not a prereq for 6.042. I expect few 6.042 students go on to take it later, and the consideration of using consistent notation has never come up. Since all sample spaces in 6.042 are discrete (countable), we do fine using summations and avoiding the complexities of measure theory, most notably the existence of non-measurable sets. On the other hand, everything we do is consistent with the measure-theoretic perspective. I hope the conflicting notation does not burden you unduly. regards, A. Barry Revzin wrote: > You guys go over a lot of definitions for expectation, but what about > the more general one ? > > Let f: X --> R+ be a random variable, the expection is integral over X > of f du, where u (mu) is the measure. > > Also, this entire section will be extremely weird since in 18.103 > (Fourier Analysis, Measure Theory) we learn the measure theory side > which has its own explanations and descriptions... and symbols. The > overlap will be confusing. > > Barry > From avalys@MIT.EDU Tue Nov 29 22:34:12 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU3YC5o008028 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 22:34:12 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU3YBr1020400 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 22:34:11 -0500 (EST) Received: from [18.96.6.172] (SIMMONS-FOUR-TWENTY-SEVEN.MIT.EDU [18.96.6.172]) (authenticated bits=0) (User authenticated as avalys@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU3Y8pp000193 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 22:34:08 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: <1B4ECB15-6AD2-4E75-BD75-8EBFF67433E6@mit.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Alex Valys Subject: 6.042: [Hanson] Required Reading Comments Date: Tue, 29 Nov 2005 22:34:07 -0500 X-Mailer: Apple Mail (2.746.2) X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1069 Content-Length: 149 X-Keywords: NonJunk NotJunk I am a little bit unclear about how to actually apply the section on expected value to actual problems. Some examples would be nice. Alex Valys From ridell@MIT.EDU Tue Nov 29 22:46:43 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU3kh5o009201 for <6042-probs@theory.csail.MIT.EDU>; Tue, 29 Nov 2005 22:46:43 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU3kgr1029909 for <6042-probs@theory.csail.MIT.EDU>; Tue, 29 Nov 2005 22:46:42 -0500 (EST) Received: from w92-130-webmail-3.mit.edu (W92-130-WEBMAIL-3.MIT.EDU [18.7.22.133]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU3kevb002780 for <6042-probs@theory.csail.MIT.EDU>; Tue, 29 Nov 2005 22:46:40 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jAU3kemD015760; Tue, 29 Nov 2005 22:46:40 -0500 Received: from AP-SEVENTY.MIT.EDU (AP-SEVENTY.MIT.EDU [18.153.1.70]) (User authenticated as ridell@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 29 Nov 2005 22:46:40 -0500 Message-ID: <20051129224640.81zt0eycgv0kkwww@webmail.mit.edu> Date: Tue, 29 Nov 2005 22:46:40 -0500 From: Rebecca Idell To: 6042-probs@theory.csail.MIT.EDU Subject: reading 13, ta: hanson MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1070 Content-Length: 260 X-Keywords: NonJunk NotJunk Can you explain more about the probability density function on page 6? Rebecca Idell -- Rebecca Idell Massachusetts Institute of Technology Electrical Engineering and Computer Science, Class of 2007 479 Commonwealth Avenue Boston, MA 02215 (617) 875-0889 From fluff@MIT.EDU Tue Nov 29 22:51:21 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU3pK5o009706 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 22:51:20 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU3odr1002789 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 22:50:39 -0500 (EST) Received: from [18.244.6.19] (SENIOR-TWO-SEVENTY-FOUR.MIT.EDU [18.244.6.19]) (authenticated bits=0) (User authenticated as fluff@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU3obYX003691 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 22:50:37 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: <4FD036DE-F425-4DAC-9F5C-664D50EB4E6B@mit.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Crystal Chao Subject: [Jelani] week 13 reading Date: Tue, 29 Nov 2005 22:48:03 -0500 X-Mailer: Apple Mail (2.746.2) X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1071 Content-Length: 324 X-Keywords: NonJunk NotJunk Everything starting from the binomial density approximation onwards went completely over my head. I think I might just have a 10-page-per- day math comprehension limit. The expected value stuff seemed understandable with the six-sided die example, but I didn't get anything after that (starting from 5.1). ~Crystal From sil_03@MIT.EDU Tue Nov 29 23:14:58 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU4Ew5o016707 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 23:14:58 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU4EvVs017835 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 23:14:57 -0500 (EST) Received: from w92-130-webmail-5.mit.edu (W92-130-WEBMAIL-5.MIT.EDU [18.7.22.136]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU4EsDT008651 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 29 Nov 2005 23:14:55 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-5.mit.edu (8.12.4) id jAU4EsAp012654; Tue, 29 Nov 2005 23:14:54 -0500 Received: from NEW-SIX-SIXTY-SIX.MIT.EDU (NEW-SIX-SIXTY-SIX.MIT.EDU [18.241.7.155]) (User authenticated as sil_03@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 29 Nov 2005 23:14:54 -0500 Message-ID: <20051129231454.gjf23zjxvn4s80ck@webmail.mit.edu> Date: Tue, 29 Nov 2005 23:14:54 -0500 From: "Silvia F. Baptista" To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] Week 13 comments MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1072 Content-Length: 210 X-Keywords: NonJunk NotJunk It is interesting that the population of the country has no effect on poll size! I don't see how. I couldn't really follow the Binomial Sampling theorem so it would be nice if we went over it again in class. From dowgun@MIT.EDU Wed Nov 30 00:00:52 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU50q5o004249 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 00:00:52 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU50oVs018961 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 00:00:50 -0500 (EST) Received: from w92-130-webmail-6.mit.edu (W92-130-WEBMAIL-6.MIT.EDU [18.7.22.137]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU50m3b017612 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 00:00:49 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-6.mit.edu (8.12.4) id jAU50mvp021786; Wed, 30 Nov 2005 00:00:48 -0500 Received: from PLP-ONE-FORTY-THREE.MIT.EDU (PLP-ONE-FORTY-THREE.MIT.EDU [18.218.1.143]) (User authenticated as dowgun@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 00:00:48 -0500 Message-ID: <20051130000048.pr7oaai2tcg8wsc4@webmail.mit.edu> Date: Wed, 30 Nov 2005 00:00:48 -0500 From: Neil M Dowgun To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] ln13 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1073 Content-Length: 404 X-Keywords: NotJunk Right, so this week's lecture notes introduced a lot of math that I can sort of follow, but I doubt if I'll be able to remember. Thus, my question for the week: do we need to remember how to derive the following formulas? e^(-n(n-1)/2d) The upper bound for PDF (#1 on page 13) The upper bound for CDF (bottom of 13) The formula for delta (#3 on page 15) and The binomial sampling equation. Thanks, Neil From ozcan@MIT.EDU Wed Nov 30 00:17:55 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU5Ht5o011114 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 00:17:55 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAU5Hsuq026577 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 00:17:54 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU5HrMN002167 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 00:17:53 -0500 (EST) Received: from ebrum.mit.edu (OZCAN.MIT.EDU [18.241.3.106]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAU5Hkol006660 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 00:17:46 -0500 (EST) Message-Id: <5.2.1.1.2.20051130001547.02263a88@po12.mit.edu> X-Sender: ozcan@hesiod (Unverified) X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 30 Nov 2005 00:17:34 -0500 To: 6042-probs@theory.csail.mit.edu From: Yasin Ozcan Subject: [hanson]reading comments Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1"; format=flowed X-Spam-Score: 3.076 X-Spam-Level: *** (3.076) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by theory.csail.mit.edu id jAU5Ht5o011114 Status: RO X-UID: 1074 Content-Length: 1827 X-Keywords: NonJunk NotJunk The section on confidence levels, and how we might interpret the confidence levels wrong, is quite interesting. Section 4: Confidence Levels Suppose a pollster uses a sample of 662 random voters to estimate the fraction of voters who prefer Clinton, and the pollster finds that 364 of them prefer Clinton. It’s tempting, but sloppy, to say that this means: False Claim. With probability 0.95, the fraction, p, of voters who prefer Clinton is 364/662±0.04. Since 364/662-0.04 > 0.50, there is a 95% chance that more than half the voters prefer Clinton. What’s objectionable about this statement is that it talks about the probability or “chance” that a real world fact is true, namely that the actual fraction, p, of voters favoring Clinton is more than 0.50. But p is what it is, and it simply makes no sense to talk about the probability that it is something else. For example, suppose p is actually 0.49; then it’s nonsense to ask about the probability that it is within 0.04 of 364/662 —it simply isn’t. A more careful summary of what we have accomplished goes this way: We have described a probabilistic procedure for estimating the value of the actual fraction, p. The probability that our estimation procedure will yield a value within 0.04 of p is 0.95. This is a bit of a mouthful, so special phrasing closer to the sloppy language is commonly used. The pollster would describe his conclusion by saying that At the 95% confidence level, the fraction of voters who prefer Clinton is 364/662± 0.04. It’s important to remember that confidence levels refer to the results of estimation procedures for real-world quantities. The real-world quantity being estimated is typically unknown, but fixed; it is not a random variable, so it makes no sense to talk about the probability that it has some property. From jjmonzon@MIT.EDU Wed Nov 30 00:34:15 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU5YF5o017894 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 00:34:15 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU5YEVs008611 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 00:34:14 -0500 (EST) Received: from JOSHDESKTOP.mit.edu (BURTON-ONE-FORTY-SIX.MIT.EDU [18.247.5.146]) (authenticated bits=0) (User authenticated as jjmonzon@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU5Y6YU023326 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 00:34:07 -0500 (EST) Message-Id: <6.2.3.4.2.20051130002706.01d0d7e8@po9.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Wed, 30 Nov 2005 00:34:10 -0500 To: 6042-probs@theory.csail.mit.edu From: "Joshua Jen C. Monzon" Subject: [David] - reading comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 3.816 X-Spam-Level: *** (3.816) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1075 Content-Length: 359 X-Keywords: NotJunk This subject matter is a bit complex but I like the examples given - some of them are a bit counterintuitive and confusing like the birthday principle. I liked the "making baby girls" example though - was funny. Josh Joshua Jen C. Monzon Massachusetts Institute of Technology Electrical Engineering with Computer Science jjmonzon@mit.edu 617-803-7497 From zacharyozer@gmail.com Wed Nov 30 00:46:24 2005 Return-Path: Received: from zproxy.gmail.com (zproxy.gmail.com [64.233.162.207]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU5kO5o024569 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 00:46:24 -0500 Received: by zproxy.gmail.com with SMTP id 13so342039nzn for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 21:46:24 -0800 (PST) DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=beta; d=gmail.com; h=received:message-id:date:from:sender:to:subject:mime-version:content-type:content-transfer-encoding:content-disposition; b=NN+FGaQWzQBs/hXj2c83BByFVfEu3JDtI2+BYqKHSyDbkqxrjslPtuY3iyYi9wariXJ3GDmxmONFJk2fPa7vrgriklZ1goY/MMlkGUd4U6sQlARgVMztubG5sLaNa2HbyJG91o0ydNRka21NTw/7zco/+ey9aX4yEqvpcXLA3XE= Received: by 10.64.220.11 with SMTP id s11mr3663412qbg; Tue, 29 Nov 2005 21:46:24 -0800 (PST) Received: by 10.65.152.13 with HTTP; Tue, 29 Nov 2005 21:46:24 -0800 (PST) Message-ID: <4f2613e50511292146q8dc62b7k4b5f45927a009b6f@mail.gmail.com> Date: Wed, 30 Nov 2005 00:46:24 -0500 From: Zachary Adam Ozer Sender: zacharyozer@gmail.com To: 6042-probs@theory.lcs.mit.edu Subject: Tutor Comments: Mean time to failure LN 13 Pg 20 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by theory.csail.mit.edu id jAU5kO5o024569 Status: RO X-UID: 1076 Content-Length: 619 X-Keywords: NotJunk I was just wondering how mean time to failure is affected by redundant systems, ie, what if I have 2 systems where one kicks in when the other fails. It seems like the probability of failure the same, since I'm still relying on an identical system, yet that doesn't make sense from a practical standpoint, since then there'd be little advantage to using redundant systems. Are they mulitiplicative? IE if the mean proabaility of failure of one system is 1/100, does the redundancy cause a mean probability of failure of (1/100)(1/100)? What about as the redundancy tends towards infinity? Just some thoughts, -zozer From bakster@MIT.EDU Wed Nov 30 00:54:10 2005 Return-Path: Received: from bexxxley.mit.edu (BEXXXLEY.MIT.EDU [18.246.1.238]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU5sA5o027136 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 00:54:10 -0500 Received: (from bakster@localhost) by bexxxley.mit.edu (8.12.9) id jAU5s70l019591; Wed, 30 Nov 2005 00:54:07 -0500 Date: Wed, 30 Nov 2005 00:54:07 -0500 (EST) From: Alexander G Bakst X-X-Sender: bakster@bexxxley To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] Week 13 Comments Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1077 Content-Length: 118 X-Status: A X-Keywords: NonJunk NotJunk This wasn't implicit in the reading I thought: if x and y are two variables, is E[xy] = E[x] * E[y]? Alexander Bakst From vixen@MIT.EDU Wed Nov 30 00:59:26 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU5xQ5o027485 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 00:59:26 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU5xPVs022523 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 00:59:25 -0500 (EST) Received: from [18.243.2.26] (WALLFLOWER.MIT.EDU [18.243.2.26]) (authenticated bits=0) (User authenticated as vixen@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU5xMdS026897 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 00:59:23 -0500 (EST) Mime-Version: 1.0 X-Sender: vixen@hesiod Message-Id: Date: Wed, 30 Nov 2005 00:57:16 -0500 To: 6042-probs@theory.lcs.mit.edu From: Amanda Seybold Subject: LN13 Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1078 Content-Length: 71 X-Status: A X-Keywords: NotJunk I don't understand the difference between events and random variables. From meyer@imap.theory.csail.mit.edu Wed Nov 30 01:06:08 2005 Message-ID: <438D4155.9010904@csail.mit.edu> Date: Wed, 30 Nov 2005 01:06:13 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Alexander G Bakst Subject: Re: [David] Week 13 Comments References: In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 315 X-UID: 1079 X-Keywords: only if X,y are independent counterexample when not independent: Let X=Y = +1 or -1 with equal probability (1/2). So E[X] = E[Y] = 0, but E[XY] = E[X^2] = 1. Alexander G Bakst wrote: > This wasn't implicit in the reading I thought: if x and y are two > variables, is E[xy] = E[x] * E[y]? > > Alexander Bakst From rshearer@MIT.EDU Wed Nov 30 01:07:49 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU67n5o003113 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:07:49 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU67mVs026797 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:07:48 -0500 (EST) Received: from [18.244.6.41] (SENIOR-TWO-NINETY-SIX.MIT.EDU [18.244.6.41]) (authenticated bits=0) (User authenticated as rshearer@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU67bBO028033 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:07:42 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v623) Content-Transfer-Encoding: 7bit Message-Id: Content-Type: text/plain; charset=US-ASCII; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Rachel Shearer Subject: [Jelani] TP13 Comments Date: Wed, 30 Nov 2005 01:07:35 -0500 X-Mailer: Apple Mail (2.623) X-Spam-Score: 3.076 X-Spam-Level: *** (3.076) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1080 Content-Length: 140 X-Keywords: NonJunk NotJunk The reading didn't explain Expected Values very well at all, and I found myself confused when doing the tutor problems. - Rachel Shearer From meyer@imap.theory.csail.mit.edu Wed Nov 30 01:09:39 2005 Message-ID: <438D4229.6020807@csail.mit.edu> Date: Wed, 30 Nov 2005 01:09:45 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Amanda Seybold Subject: Re: LN13 References: In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 306 X-UID: 1081 X-Keywords: give me a hint where your understanding fails. for a start, an event is a set (of outcomes, that is, points in the sample space), while an RV is a function (from outcomes to whatever you want). regards, A. Amanda Seybold wrote: > I don't understand the difference between events and random variables. From rnjacobs@MIT.EDU Wed Nov 30 01:11:32 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU6BW5o004097 for <6042-probs@theory.csail.MIT.EDU>; Wed, 30 Nov 2005 01:11:32 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAU6BVuq018208 for <6042-probs@theory.csail.MIT.EDU>; Wed, 30 Nov 2005 01:11:31 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU6BVMN003817 for <6042-probs@theory.csail.MIT.EDU>; Wed, 30 Nov 2005 01:11:31 -0500 (EST) Received: from white-meteo.mit.edu (WHITE-METEO.MIT.EDU [18.243.0.221]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAU6BRok008936 for <6042-probs@theory.csail.MIT.EDU>; Wed, 30 Nov 2005 01:11:28 -0500 (EST) Received: (from rnjacobs@localhost) by white-meteo.mit.edu (8.12.9) id jAU6BRIj002845; Wed, 30 Nov 2005 01:11:27 -0500 Message-Id: <200511300611.jAU6BRIj002845@white-meteo.mit.edu> To: 6042-probs@theory.csail.MIT.EDU Subject: [Jelani] Reading response Date: Wed, 30 Nov 2005 01:11:27 -0500 From: r n jacobs X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1082 Content-Length: 168 X-Keywords: NonJunk NotJunk Nope, no comments. I still remember most of my 041. (A review of continuous probability would be nice but apparently will not be covered in 042...) - Robert Jacobs From sergiob@MIT.EDU Wed Nov 30 01:17:28 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU6HS5o008719 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 01:17:28 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU6HRVs001738 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 01:17:27 -0500 (EST) Received: from mit-kf7uwcnbdr4.mit.edu (SENIOR-FORTY-SIX.MIT.EDU [18.244.5.46]) (authenticated bits=0) (User authenticated as sergiob@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU6HNv8029099 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 01:17:24 -0500 (EST) Message-Id: <5.2.1.1.2.20051129231507.028c3a48@po14.mit.edu> X-Sender: sergiob@po14.mit.edu X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Tue, 29 Nov 2005 23:17:21 -0700 To: 6042-probs@theory.csail.mit.edu From: Sergio Bacallado Subject: [David] Week 13 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1083 Content-Length: 202 X-Keywords: NonJunk NotJunk I liked the part about confidence. It's a very useful concept in every-day experimental calculations. Probability doesn't cease to amaze me; intuition can be so misleading. Sergio Bacallado Group 1 From yaser@MIT.EDU Wed Nov 30 01:21:31 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU6LV5o009181 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:21:31 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU6LTVs003714 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:21:29 -0500 (EST) Received: from Charizard (NEW-SEVEN-THIRTY-ONE.MIT.EDU [18.241.7.220]) (authenticated bits=0) (User authenticated as ykhan@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU6LNe5029473 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:21:23 -0500 (EST) Message-Id: <200511300621.jAU6LNe5029473@outgoing.mit.edu> From: "Yaser Khan" To: <6042-probs@theory.lcs.mit.edu> Subject: David: tp13 reading comments Date: Wed, 30 Nov 2005 01:21:25 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0066_01C5F54C.620520B0" X-Mailer: Microsoft Office Outlook, Build 11.0.6353 Thread-Index: AcX1dkpdNbG+04S4To6Zc0pFYhTlqg== X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: 2.706 X-Spam-Level: ** (2.706) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1084 Content-Length: 5323 X-Status: A X-Keywords: NonJunk NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_0066_01C5F54C.620520B0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Hi David, As a whole, the reading was a bit dense with formulas, to the extent that I keep getting similar definitions mixed up (for instance the distinctions between the distributions). However, my question is: will we be concerned with the t, poisson, or chi distributions in terms of random variables? Thanks! _Yaser ------=_NextPart_000_0066_01C5F54C.620520B0 Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: quoted-printable

Hi = David,

 

As a whole, the reading was a bit = dense with formulas, to the extent that I keep getting similar definitions = mixed up (for instance the distinctions between the distributions). However, my = question is: will we be concerned with the t, poisson, or chi distributions in terms of random variables?


Thanks!

 

_Yaser

------=_NextPart_000_0066_01C5F54C.620520B0-- From ereid@MIT.EDU Wed Nov 30 01:28:15 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU6SF5o013634 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:28:15 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU6SEVs007208 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:28:14 -0500 (EST) Received: from [18.242.6.198] (NEXT-FOUR-FIFTY-THREE.MIT.EDU [18.242.6.198]) (authenticated bits=0) (User authenticated as ereid@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU6SCcG000155 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:28:12 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v734) Content-Transfer-Encoding: 7bit Message-Id: <49EAF327-2A3E-4CBD-8256-5E5E11D9E729@MIT.EDU> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Elizabeth Reid Subject: [Hanson] Reading comments Date: Wed, 30 Nov 2005 01:28:09 -0500 X-Mailer: Apple Mail (2.734) X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1085 Content-Length: 397 X-Status: A X-Keywords: NonJunk NotJunk I was initially surprised (and skeptical) about the numbers game strategy, but its proof makes sense. I guess my only question would be how to pick the "x" you hope is between L and H, but that's just a matter of personal opinion. :) Oh, and did you get my reading comments last week? You never responded, and the 6042-probs list was acting oddly when I tried to email it... Elizabeth From mpapi@MIT.EDU Wed Nov 30 01:28:44 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU6Si5o013662 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:28:44 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU6SgVs007504 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:28:43 -0500 (EST) Received: from [192.168.0.2] (MPAPI.MIT.EDU [18.239.4.219]) (authenticated bits=0) (User authenticated as mpapi@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU6Sa1N000217 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:28:40 -0500 (EST) Subject: [Jelani] Week 13 comments From: Matt Papi To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Wed, 30 Nov 2005 01:28:35 -0500 Message-Id: <1133332115.8490.4.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.2.3 (2.2.3-2.fc4) Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1086 Content-Length: 320 X-Keywords: NonJunk NotJunk Section 3, particularly the calculations performed on pages 15 and 16 - I could definitely use a clearer explanation of polling and confidence levels in lecture. I also feel that the notes weren't very helpful with the last tutorial problem, but reading the answer to the problem after submitting helped a lot. - Matt From kevin08@MIT.EDU Wed Nov 30 01:46:13 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU6kD5o019936 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:46:13 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU6kCVs017058 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:46:12 -0500 (EST) Received: from kevlar.mit.edu (NEXT-THREE-FIFTY-SEVEN.MIT.EDU [18.242.6.102]) (authenticated bits=0) (User authenticated as kevin08@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU6k9AE002004 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 01:46:10 -0500 (EST) Message-Id: <6.2.3.4.2.20051130014533.02a5f6f0@po10.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Wed, 30 Nov 2005 01:46:08 -0500 To: 6042-probs@theory.lcs.mit.edu From: Kevin Wang Subject: [Hanson] Reading Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1087 Content-Length: 120 X-Keywords: NonJunk NotJunk Hi, I was curious about where the entropy function H(a) came originated from (Section 3.4.2, Pg. 12). Thanks. Kevin From meyer@imap.theory.csail.mit.edu Wed Nov 30 01:54:55 2005 Message-ID: <438D4CC5.1060700@csail.mit.edu> Date: Wed, 30 Nov 2005 01:55:01 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Amanda Seybold Subject: Re: LN13 References: <438D4229.6020807@csail.mit.edu> In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 832 X-UID: 1088 X-Keywords: Sure they are related: events correspond (via indicator variables defined in Notes 13) to zero-one valued RV's, so they are essentially a special case of RV's. Conversely, with an RV, R, and value v, there is an event [R=v] consisting of those outcomes w such that R(w)=v. So you could specify an RV by giving all the events [R=v]. Is it clearer now? regards, A. Amanda Seybold wrote: > It seems like they are expressing the same idea: creating a set of > outcomes with something in common. > >> give me a hint where your understanding fails. for a start, an event >> is a set (of outcomes, that is, points in the sample space), while an >> RV is a function (from outcomes to whatever you want). >> regards, A. >> >> Amanda Seybold wrote: >> >>> I don't understand the difference between events and random variables. From meyer@imap.theory.csail.mit.edu Wed Nov 30 01:11:50 2005 Return-Path: Received: from rozz.csail.mit.edu (mail@rozz.csail.mit.edu [128.30.2.16]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU6Bo5o004154 for ; Wed, 30 Nov 2005 01:11:50 -0500 Received: from biscayne-one-station.mit.edu ([18.7.7.80]) by rozz.csail.mit.edu with esmtps (TLSv1:AES256-SHA:256) (Exim 4.50) id 1EhLC2-0004gr-2S for meyer@csail.mit.edu; Wed, 30 Nov 2005 01:11:50 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU6BmVs028827 for ; Wed, 30 Nov 2005 01:11:48 -0500 (EST) Received: from [18.243.2.26] (WALLFLOWER.MIT.EDU [18.243.2.26]) (authenticated bits=0) (User authenticated as vixen@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU6Bf1s028494 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for ; Wed, 30 Nov 2005 01:11:41 -0500 (EST) Mime-Version: 1.0 X-Sender: vixen@hesiod Message-Id: In-Reply-To: <438D4229.6020807@csail.mit.edu> References: <438D4229.6020807@csail.mit.edu> Date: Wed, 30 Nov 2005 01:09:34 -0500 To: "Prof. Albert R. Meyer" From: Amanda Seybold Subject: Re: LN13 Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Spam-Score: 1.217 X-Scanned-By: MIMEDefang 2.42 X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on theory.csail.mit.edu X-Spam-Level: X-Spam-Status: No, hits=-4.9 required=3.7 tests=AWL,BAYES_00 autolearn=ham version=2.63 Status: RO X-Status: A Content-Length: 415 X-UID: 1089 X-Keywords: NotJunk It seems like they are expressing the same idea: creating a set of outcomes with something in common. >give me a hint where your understanding fails. for a start, an >event is a set (of outcomes, that is, points in the sample space), >while an RV is a function (from outcomes to whatever you want). >regards, A. > >Amanda Seybold wrote: >>I don't understand the difference between events and random variables. From meyer@imap.theory.csail.mit.edu Wed Nov 30 02:00:22 2005 Message-ID: <438D4E0C.4080406@csail.mit.edu> Date: Wed, 30 Nov 2005 02:00:28 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Elizabeth Reid Subject: Re: [Hanson] Reading comments References: <49EAF327-2A3E-4CBD-8256-5E5E11D9E729@MIT.EDU> In-Reply-To: <49EAF327-2A3E-4CBD-8256-5E5E11D9E729@MIT.EDU> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 614 X-UID: 1090 X-Keywords: most recent email comment we have for you is 11/17. if you have a copy of last weeks, send it now. (It would help if you include the TP# in the subject line.) regards, A. Elizabeth Reid wrote: > I was initially surprised (and skeptical) about the numbers game > strategy, but its proof makes sense. I guess my only question would be > how to pick the "x" you hope is between L and H, but that's just a > matter of personal opinion. :) > > Oh, and did you get my reading comments last week? You never responded, > and the 6042-probs list was acting oddly when I tried to email it... > > Elizabeth From hkhall@MIT.EDU Wed Nov 30 02:10:20 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU7AK5o026614 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 02:10:20 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU7AIKa027484; Wed, 30 Nov 2005 02:10:18 -0500 (EST) Received: from [18.96.6.209] (SIMMONS-FOUR-SIXTY-FOUR.MIT.EDU [18.96.6.209]) (authenticated bits=0) (User authenticated as hkhall@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU7AFtN003948 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT); Wed, 30 Nov 2005 02:10:16 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v623) Content-Type: text/plain; charset=US-ASCII; format=flowed Message-Id: <6fe524b5cc90d96d530e7b06be446ee8@mit.edu> Content-Transfer-Encoding: 7bit From: Harrison King Hall Subject: [David] Week 13 Comments Date: Wed, 30 Nov 2005 02:10:17 -0500 To: 6042-probs@theory.csail.mit.edu X-Mailer: Apple Mail (2.623) X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1091 Content-Length: 646 X-Keywords: NotJunk David- Well syntactically I am doing better this week. I am having some major problems though, primarily with approximating the binomial density function and the applications that follow. I understand the formula as it is just plug and chug, it is its roots that I do not understand, however. I would like to see a formal definition of where it comes from if it is not beyond the scope of the class. From there I really didn't understand any of the equivalencies used in determining the polling but that is probably because it is my first time through the material. I hope we go over some of this stuff in class tomorrow. -Harrison From rshroff@MIT.EDU Wed Nov 30 02:13:50 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU7Do5o027071 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 02:13:50 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU7DmKa029084 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 02:13:48 -0500 (EST) Received: from w92-130-webmail-1.mit.edu (W92-130-WEBMAIL-1.MIT.EDU [18.7.22.131]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU7DgsG004194 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 02:13:42 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-1.mit.edu (8.12.4) id jAU7DgeW022350; Wed, 30 Nov 2005 02:13:42 -0500 Received: from NEXT-THREE-TWENTY.MIT.EDU (NEXT-THREE-TWENTY.MIT.EDU [18.242.6.65]) (User authenticated as rshroff@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 02:13:42 -0500 Message-ID: <20051130021342.s448jmsvqhc8kgw4@webmail.mit.edu> Date: Wed, 30 Nov 2005 02:13:42 -0500 From: rshroff@MIT.EDU To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] Reading Assignment MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -0.149 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1092 Content-Length: 122 X-Keywords: NonJunk NotJunk I was wondering if we could go over the approximation to the binomial distribution in some detail. Thanks, Rahul Shroff From lkini@MIT.EDU Wed Nov 30 02:17:36 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU7Ha5o030988 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 02:17:36 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU7HZKa000828 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 02:17:35 -0500 (EST) Received: from [18.239.6.94] (MACGREGOR-THREE-FORTY-NINE.MIT.EDU [18.239.6.94]) (authenticated bits=0) (User authenticated as lkini@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU7HWWW004486 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 02:17:33 -0500 (EST) Message-ID: <438D5200.1050608@mit.edu> Date: Wed, 30 Nov 2005 02:17:20 -0500 From: Lohith Kini User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [Hanson] Week 13 Lecture Notes Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1093 Content-Length: 206 X-Keywords: NonJunk NotJunk Hi Hanson, I was a little confused about approximating cumulative binomial distribution functions, especially the caveat (Section 3.5, page 13). How does thinking it in complementary terms help? Lohith From jstritar@MIT.EDU Wed Nov 30 02:21:09 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU7L95o031553 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 02:21:09 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU7L8Ka002255 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 02:21:08 -0500 (EST) Received: from BAKER-THREE-NINETY-EIGHT.MIT.EDU (BAKER-THREE-NINETY-EIGHT.MIT.EDU [18.245.6.143]) (authenticated bits=0) (User authenticated as jstritar@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU7L6aX004705 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 02:21:06 -0500 (EST) Subject: [Sayan] Reading comments From: Jon Stritar To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Wed, 30 Nov 2005 02:21:06 -0500 Message-Id: <1133335266.13472.2.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.4.1 Content-Transfer-Encoding: 7bit X-Spam-Score: 3.076 X-Spam-Level: *** (3.076) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1094 Content-Length: 148 X-Keywords: NonJunk NotJunk 3.3 The Numbers game I thought the winning strategy for this was interesting. It is not very intuitive... but it still makes sense. Jon Stritar From dnreshef@MIT.EDU Wed Nov 30 02:46:10 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU7k95o002670 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 02:46:09 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU7k8Ka012896 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 02:46:08 -0500 (EST) Received: from w92-130-webmail-1.mit.edu (W92-130-WEBMAIL-1.MIT.EDU [18.7.22.131]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU7k2If006455 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 02:46:02 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-1.mit.edu (8.12.4) id jAU7k2dA024166; Wed, 30 Nov 2005 02:46:02 -0500 Received: from MACGREGOR-EIGHTY-SIX.MIT.EDU (MACGREGOR-EIGHTY-SIX.MIT.EDU [18.239.5.86]) (User authenticated as dnreshef@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 02:46:02 -0500 Message-ID: <20051130024602.m7txa136ae80sowo@webmail.mit.edu> Date: Wed, 30 Nov 2005 02:46:02 -0500 From: David N Reshef To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] Reading Comments 13 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -1.11 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1095 Content-Length: 182 X-Keywords: I found the binomial distribution concepts and their applications (especially to polling) particularly interesting. Also, could we go over confidence levels in class? Thanks, -Dave From ctsims@MIT.EDU Wed Nov 30 03:34:55 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU8Yt5o021434 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 03:34:55 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU8YsKa003017 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 03:34:54 -0500 (EST) Received: from HowardRoark.mit.edu (EASTCAMPUS-NINE-TWENTY-SEVEN.MIT.EDU [18.238.6.160]) (authenticated bits=0) (User authenticated as ctsims@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU8Yp31009221 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 03:34:52 -0500 (EST) Message-Id: <5.2.1.1.2.20051130031809.01ea6ee8@po12.mit.edu> X-Sender: ctsims@po12.mit.edu X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 30 Nov 2005 03:32:11 -0500 To: 6042-probs@theory.lcs.mit.edu From: Clayton Sims Subject: [6042] Weekly reading problem - Clayton Sims Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1096 Content-Length: 190 X-Keywords: NonJunk NotJunk I found that the section on page 18 about expected values could use more examples about the use of expected values with variables. I would like to see that presented in class. -Clayton From arup@MIT.EDU Wed Nov 30 03:44:46 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU8ik5o022038 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 03:44:46 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU8ijKa006868 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 03:44:45 -0500 (EST) Received: from [18.247.5.179] (BURTON-ONE-SEVENTY-NINE.MIT.EDU [18.247.5.179]) (authenticated bits=0) (User authenticated as arup@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU8iasE009664 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 03:44:38 -0500 (EST) Message-ID: <438D663B.1000605@mit.edu> Date: Wed, 30 Nov 2005 03:43:39 -0500 From: Arup Sarma User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.csail.mit.edu Subject: [Jelani] Week 13 Comments Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1097 Content-Length: 197 X-Keywords: NotJunk Section 3.4.2: I'm kindof confused as to where the approximation for the binomial density function came from, so it would be nice if it were explained in a little more detail in lecture. |Arup| From bilodeau@MIT.EDU Wed Nov 30 04:03:09 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU9395o032050 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 04:03:09 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU938Ka014136 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 04:03:08 -0500 (EST) Received: from pbilodeau (MACGREGOR-TWO-TWENTY-ONE.MIT.EDU [18.239.5.221]) (authenticated bits=0) (User authenticated as bilodeau@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU936a4010510 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 04:03:06 -0500 (EST) Message-Id: <200511300903.jAU936a4010510@outgoing.mit.edu> From: "Peter Bilodeau" To: <6042-probs@theory.lcs.mit.edu> Subject: [jelani] reading comments Date: Wed, 30 Nov 2005 04:02:48 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0000_01C5F562.ED6FBB90" X-Mailer: Microsoft Office Outlook, Build 11.0.5510 Thread-Index: AcX1jNWZoMjh2+8rQ/K5DrefiWE59A== X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: 2.779 X-Spam-Level: ** (2.779) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1098 Content-Length: 2152 X-Keywords: NonJunk NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C5F562.ED6FBB90 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit For this week's reading the most confusing part was probably the part on confidence, or possibly the approximations for the binomial distributions. Beyond that a lot of this seems understandable. Peter Bilodeau ------=_NextPart_000_0000_01C5F562.ED6FBB90 Content-Type: text/html; charset="us-ascii" Content-Transfer-Encoding: quoted-printable

For this week’s reading the most confusing part = was probably the part on confidence, or possibly the approximations for the binomial distributions.  Beyond that a lot of this seems = understandable.

 

Peter Bilodeau

------=_NextPart_000_0000_01C5F562.ED6FBB90-- From tonyng@MIT.EDU Wed Nov 30 04:46:54 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU9ks5o019424 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 04:46:54 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU9krKa001193 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 04:46:53 -0500 (EST) Received: from TNG.mit.edu (BURTON-NINETY-TWO.MIT.EDU [18.247.5.92]) (authenticated bits=0) (User authenticated as tonyng@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU9ko0A012069 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 04:46:51 -0500 (EST) Message-Id: <5.2.1.1.2.20051130044258.02144200@po9.mit.edu> X-Sender: tonyng@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 30 Nov 2005 04:46:51 -0500 To: 6042-probs@theory.lcs.mit.edu From: Tony Ng Subject: [Jelani] Reading Comments Week 13 Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1099 Content-Length: 372 X-Keywords: NotJunk I found "The Numbers Game" (Section 3.3, starting on pg8) interesting. I doesn't seem intuitive at all that selecting a number at random can help make me more likely to win the game. It almost seems like it is the same as choosing one of the two numbers at random, but it's surprising that the math works out to show that it is in fact a winning strategy. - Tony Ng From kjhollen@MIT.EDU Wed Nov 30 04:48:22 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAU9mM5o021188 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 04:48:22 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAU9mLKa001754 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 04:48:21 -0500 (EST) Received: from w92-130-webmail-3.mit.edu (W92-130-WEBMAIL-3.MIT.EDU [18.7.22.133]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAU9mEnc012106 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 04:48:15 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jAU9mE7s011240; Wed, 30 Nov 2005 04:48:14 -0500 Received: from dhcp-23-135.media.mit.edu (dhcp-23-135.media.mit.edu [18.85.23.135]) (User authenticated as kjhollen@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 04:48:14 -0500 Message-ID: <20051130044814.v9fna3ft6ylcoo40@webmail.mit.edu> Date: Wed, 30 Nov 2005 04:48:14 -0500 From: Kate Hollenbach To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] numbers game MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1100 Content-Length: 51 X-Keywords: NonJunk NotJunk the numbers game is a neat example (p. 8-9). Kate From benlu@MIT.EDU Wed Nov 30 05:02:42 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUA2g5o005812 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 05:02:42 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUA2fYn006357 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 05:02:41 -0500 (EST) Received: from [18.244.3.46] (CAPSAICIN.MIT.EDU [18.244.3.46]) (authenticated bits=0) (User authenticated as benlu@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUA2YKd012637 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 05:02:35 -0500 (EST) Message-ID: <438D78C1.8070701@mit.edu> Date: Wed, 30 Nov 2005 05:02:41 -0500 From: Benjamin Lu Organization: MIT User-Agent: Mozilla Thunderbird 1.0.7 (X11/20051013) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [Jelani][6.042] comments on reading 13 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1101 Content-Length: 207 X-Keywords: NotJunk My eyes definitely started to glaze over during the section on polling and confidence intervals. Also, the online tutor problem took me forever. It would be great to go over those topics in lecture. ~Ben From lana@MIT.EDU Wed Nov 30 06:50:19 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUBoJ5o030431 for <6042-probs@theory.csail.MIT.EDU>; Wed, 30 Nov 2005 06:50:19 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUBoIYn016238 for <6042-probs@theory.csail.MIT.EDU>; Wed, 30 Nov 2005 06:50:18 -0500 (EST) Received: from w92-130-webmail-2.mit.edu (W92-130-WEBMAIL-2.MIT.EDU [18.7.22.132]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUBoBXp017405 for <6042-probs@theory.csail.MIT.EDU>; Wed, 30 Nov 2005 06:50:12 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jAUBoBv3019842; Wed, 30 Nov 2005 06:50:11 -0500 Received: from NEXT-FIVE-SIXTY-NINE.MIT.EDU (NEXT-FIVE-SIXTY-NINE.MIT.EDU [18.242.7.58]) (User authenticated as lana@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 06:50:11 -0500 Message-ID: <20051130065011.sd7hi6fte84k8kcw@webmail.mit.edu> Date: Wed, 30 Nov 2005 06:50:11 -0500 From: Svetlana Goldenberg To: 6042-probs@theory.csail.MIT.EDU Subject: [Sayan] TP 12 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1102 Content-Length: 171 X-Status: A X-Keywords: NonJunk NotJunk The part I found the most intriguing was the halting problem, and the intuitive feeling that it must have some kind of an answer. Can it be modeled by Markov chains? Lana From kromer@MIT.EDU Wed Nov 30 09:51:22 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUEpL5o003189 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 09:51:21 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUEpKrd027347 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 09:51:20 -0500 (EST) Received: from m56-129-21.mit.edu (M56-129-21.MIT.EDU [18.56.0.50]) (authenticated bits=56) (User authenticated as kromer@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUEpDct029021 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 09:51:14 -0500 (EST) Received: (from kromer@localhost) by m56-129-21.mit.edu (8.12.9) id jAUEpDqa032749; Wed, 30 Nov 2005 09:51:13 -0500 Subject: [David] Email comments for reading From: Katherine Romer To: 6042-probs@theory.lcs.MIT.EDU Content-Type: text/plain Content-Transfer-Encoding: 7bit Date: Wed, 30 Nov 2005 09:51:13 -0500 Message-Id: <1133362273.32582.2.camel@m56-129-21.mit.edu> Mime-Version: 1.0 X-Mailer: Evolution 2.0.4 X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1103 Content-Length: 233 X-Keywords: NotJunk p.21 "If every couple follows the strategy of having children until they get a girl, what will eventually happen to the fraction of girls born in this world?" Will it remain the same (because each couple expects to have 2 children)? From veracarr@MIT.EDU Wed Nov 30 10:12:41 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFCf5o017167 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:12:41 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFCeP6007599 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:12:40 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFCdaT020862 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:12:39 -0500 (EST) Received: from [18.245.6.197] (BAKER-FOUR-FIFTY-TWO.MIT.EDU [18.245.6.197]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAUFCaok005040 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:12:37 -0500 (EST) Message-ID: <438DC199.6040400@mit.edu> Date: Wed, 30 Nov 2005 10:13:29 -0500 From: Vera Carr User-Agent: Mozilla Thunderbird 1.0.2 (Windows/20050317) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [Hanson] Random Variables, Distributions, and Expectations Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1104 Content-Length: 112 X-Keywords: NotJunk If we could cover when we would use each of the distributions and there importance, that would be very useful. From rian@MIT.EDU Wed Nov 30 10:20:12 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFKC5o022697 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:20:12 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFKBrd003291 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:20:11 -0500 (EST) Received: from [10.0.1.2] (c-24-218-218-5.hsd1.ma.comcast.net [24.218.218.5]) (authenticated bits=0) (User authenticated as rian@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFK4nm013970 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:20:04 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: <6532AE49-7541-4E9E-882C-F6F51C02FA3D@mit.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Rian Hunter Subject: [jelani] email comments Date: Wed, 30 Nov 2005 10:19:55 -0500 X-Mailer: Apple Mail (2.746.2) X-Spam-Score: 3.076 X-Spam-Level: *** (3.076) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1105 Content-Length: 258 X-Keywords: NotJunk In the part that is the "Analysis of the Winning Strategy" 3.3.2 what if you have different probabilities for each event, for instance not 50-50? I don't exactly understand the variable assignments for not 50-50 tree probabilities. Thanks rian hunter From cbossard@MIT.EDU Wed Nov 30 10:26:01 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFQ15o027229 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:26:01 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFPxrd010254 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:25:59 -0500 (EST) Received: from w92-130-webmail-5.mit.edu (W92-130-WEBMAIL-5.MIT.EDU [18.7.22.136]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFPr7I016712 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:25:54 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-5.mit.edu (8.12.4) id jAUFPrKP026861; Wed, 30 Nov 2005 10:25:53 -0500 Received: from NEXT-TWO-SEVENTEEN.MIT.EDU (NEXT-TWO-SEVENTEEN.MIT.EDU [18.242.5.217]) (User authenticated as cbossard@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 10:25:53 -0500 Message-ID: <20051130102553.cz8cvon92j9c0okw@webmail.mit.edu> Date: Wed, 30 Nov 2005 10:25:53 -0500 From: cbossard@MIT.EDU To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] Week 13 reading comments MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -1.638 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1106 Content-Length: 95 X-Keywords: NonJunk NotJunk I'm really not sure what to ask. The distribution stuff seems a little tricky though. Cynthia From hmzhou@blackbird.csail.mit.edu Wed Nov 30 10:27:07 2005 Return-Path: Received: from blackbird.csail.mit.edu (blackbird.csail.mit.edu [128.30.51.72]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFR75o027613; Wed, 30 Nov 2005 10:27:07 -0500 Received: from blackbird.csail.mit.edu (localhost.localdomain [127.0.0.1]) by blackbird.csail.mit.edu (8.13.4/8.13.4) with ESMTP id jAUFR7aq015328; Wed, 30 Nov 2005 10:27:07 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jAUFR6Yv015325; Wed, 30 Nov 2005 10:27:07 -0500 Date: Wed, 30 Nov 2005 10:27:06 -0500 (EST) From: Hanson Zhou To: Lohith Kini cc: 6042-probs@theory.lcs.mit.edu Subject: Re: [Hanson] Week 13 Lecture Notes In-Reply-To: <438D5200.1050608@mit.edu> Message-ID: References: <438D5200.1050608@mit.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1107 Content-Length: 802 X-Status: A X-Keywords: NotJunk Hi...I think it's saying that in the case a > p, the formula does not hold (since the geometric sum does not hold). But if we look at tails instead of heads, then we can calculate 1-Pr[>=(1-a)n tails] to get the CDF we want(note that now the fraction is 1-a). The probability of a tail is 1-p and we have 1-a < 1-p by assumption. Then, we can do a similar analysis/formula to approximate Pr[>=(1-a)n tails]. You might want to check it or ask Prof. Meyer since lots of details are omitted here, but I think that's the right idea. -Hanson On Wed, 30 Nov 2005, Lohith Kini wrote: > Hi Hanson, > > I was a little confused about approximating cumulative binomial > distribution functions, especially the caveat (Section 3.5, page 13). > How does thinking it in complementary terms help? > > Lohith > From petek@MIT.EDU Wed Nov 30 10:29:12 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFTC5o031445 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:29:12 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFTArd013954 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:29:11 -0500 (EST) Received: from [128.30.5.207] (30-5-207.wireless.csail.mit.edu [128.30.5.207]) (authenticated bits=0) (User authenticated as petek@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFT3t0018267 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:29:03 -0500 (EST) Message-ID: <438DC549.2080006@mit.edu> Date: Wed, 30 Nov 2005 10:29:13 -0500 From: Pete Kruskall User-Agent: Mozilla Thunderbird 0.8 (Windows/20040913) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [Jelani] This Week's Notes Content-Type: multipart/alternative; boundary="------------050103050002020207060103" X-Spam-Score: 1.928 X-Spam-Level: * (1.928) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1108 Content-Length: 1736 X-Keywords: NonJunk NotJunk This is a multi-part message in MIME format. --------------050103050002020207060103 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit I'm up for hearing more on probability distributions and also about something that Ronnitt talked about last lecture to our breakout group. There is some complication in assigning a probability to whether a certain person prefers a candidate....something about it being either 1 or 0. Want to have that expanded a bit. -P -- Pete Kruskall 28 The Fenway Boston, MA 02215 ::::::::::::::::::::::::::::: 617.536.9925 :::Sigma Nu::::: 508.843.5861 ::::Cell Phone:: ::::http://tege.mit.edu:::::: --------------050103050002020207060103 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit I'm up for hearing more on probability distributions and also about something that Ronnitt talked about last lecture to our breakout group.  There is some complication in assigning a probability to whether a certain person prefers a candidate....something about it being either 1 or 0.  Want to have that expanded a bit. 

-P
 
-- 
Pete Kruskall
28 The Fenway
Boston, MA 02215

:::::::::::::::::::::::::::::
617.536.9925 :::Sigma Nu:::::
508.843.5861 ::::Cell Phone::
::::http://tege.mit.edu::::::
--------------050103050002020207060103-- From lmccart@MIT.EDU Wed Nov 30 10:38:00 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFbx5o002083 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:37:59 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFbwrd024913 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:37:58 -0500 (EST) Received: from w92-130-webmail-3.mit.edu (W92-130-WEBMAIL-3.MIT.EDU [18.7.22.133]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFbpI2022835 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:37:52 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jAUFbp4i005880; Wed, 30 Nov 2005 10:37:51 -0500 Received: from AP-FIFTY-ONE.MIT.EDU (AP-FIFTY-ONE.MIT.EDU [18.153.1.51]) (User authenticated as lmccart@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 10:37:51 -0500 Message-ID: <20051130103751.ja0lxrqf2vww0kw0@webmail.mit.edu> Date: Wed, 30 Nov 2005 10:37:51 -0500 From: Lauren McCarthy To: 6042-probs@theory.lcs.MIT.EDU Subject: [david] reading comments MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -1.11 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1109 Content-Length: 125 X-Keywords: NotJunk I did not find anything particularly confusing about this reading. I found the Birthday Principle most interesting. -lauren From meyer@imap.theory.csail.mit.edu Wed Nov 30 10:40:25 2005 Message-ID: <438DC7E8.6060501@csail.mit.edu> Date: Wed, 30 Nov 2005 10:40:24 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Svetlana Goldenberg Subject: Re: [Sayan] TP 12 References: <20051130065011.sd7hi6fte84k8kcw@webmail.mit.edu> In-Reply-To: <20051130065011.sd7hi6fte84k8kcw@webmail.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 347 Status: RO X-UID: 1110 X-Keywords: This week it's Notes and TP 13. The Halting Problem is covered in 6.045 and 16.840 and, best of all :-) my course 6.044. regards, A. Svetlana Goldenberg wrote: >The part I found the most intriguing was the halting problem, and the intuitive >feeling that it must have some kind of an answer. Can it be modeled by Markov >chains? >Lana > > From cvnguyen@MIT.EDU Wed Nov 30 10:40:33 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFeX5o004093 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:40:33 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFeWrd028044 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:40:32 -0500 (EST) Received: from MULTIVAC (EASTCAMPUS-SIX-SIXTY.MIT.EDU [18.238.5.149]) (authenticated bits=0) (User authenticated as cvnguyen@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFePtR024028 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:40:25 -0500 (EST) Message-ID: <002501c5f5c4$62ebc1a0$9505ee12@addressisp.com> From: "Chieu Nguyen" To: <6042-probs@theory.lcs.mit.edu> Subject: [Jelani] Week 13 comments Date: Wed, 30 Nov 2005 10:40:26 -0500 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: 1.199 X-Spam-Level: * (1.199) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1111 Content-Length: 425 X-Keywords: NotJunk (page 21) If every couple has children until getting a girl, the fraction of girls in the world does not change (if we ignore factors that may affect children of different genders differently... disease, abortion, infanticide, etc.). This is interesting. Though the fraction remains the same, the fact that each nuclear family has one and only one girl may introduce some interesting social issues.... --Chieu Nguyen From meyer@imap.theory.csail.mit.edu Wed Nov 30 10:43:52 2005 Message-ID: <438DC8B8.5060607@csail.mit.edu> Date: Wed, 30 Nov 2005 10:43:52 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Hanson Zhou CC: Lohith Kini Subject: Re: [Hanson] Week 13 Lecture Notes References: <438D5200.1050608@mit.edu> In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 1011 Status: RO X-UID: 1112 X-Keywords: yeah, that's right. the condition a>p is necessary technically, but because of the complement trick (look at tails), it is not a limitation. regards, A. Hanson Zhou wrote: >Hi...I think it's saying that in the case a > p, the formula does not hold >(since the geometric sum does not hold). But if we look at tails instead >of heads, then we can calculate 1-Pr[>=(1-a)n tails] to get the CDF we >want(note that now the fraction is 1-a). The probability of a tail is 1-p >and we have 1-a < 1-p by assumption. Then, we can do a similar >analysis/formula to approximate Pr[>=(1-a)n tails]. You might want to >check it or ask Prof. Meyer since lots of details are omitted here, but I >think that's the right idea. > >-Hanson > >On Wed, 30 Nov 2005, Lohith Kini wrote: > > > >>Hi Hanson, >> >>I was a little confused about approximating cumulative binomial >>distribution functions, especially the caveat (Section 3.5, page 13). >>How does thinking it in complementary terms help? >> >>Lohith >> >> >> From meyer@imap.theory.csail.mit.edu Wed Nov 30 05:52:46 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUAqk5o001112 for <6042-webmaster@theory.csail.mit.edu>; Wed, 30 Nov 2005 05:52:46 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUAqjYn024290 for <6042-webmaster@theory.csail.mit.edu>; Wed, 30 Nov 2005 05:52:45 -0500 (EST) Received: from SENIOR-THREE-TWENTY-ONE.MIT.EDU (SENIOR-THREE-TWENTY-ONE.MIT.EDU [18.244.6.66]) (authenticated bits=0) (User authenticated as medrano@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUAqZst014501 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-webmaster@theory.csail.mit.edu>; Wed, 30 Nov 2005 05:52:38 -0500 (EST) Subject: [sayan] probability From: Jesus Medrano To: 6042-webmaster@theory.csail.mit.edu Content-Type: text/plain Date: Wed, 30 Nov 2005 05:52:32 +0000 Message-Id: <1133329953.10283.2.camel@localhost> Mime-Version: 1.0 X-Mailer: Evolution 2.2.3 Content-Transfer-Encoding: 7bit X-Spam-Score: 1.695 X-Spam-Level: * (1.695) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO Content-Length: 319 X-UID: 1113 X-Keywords: NotJunk I'm still uncertain about the theorem in the notes about the binomial sampling. What does this mean? Is it true that only 600 people are needed to be sampled out of any size n population to get an accurate view of the entire population. This does not seem very reasonable? Is this done in practice? Jesus Medrano From mukkala@MIT.EDU Wed Nov 30 10:48:49 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFmn5o006596 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 10:48:49 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFmlrd008682 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 10:48:47 -0500 (EST) Received: from PRAVEENPAMIDI.mit.edu (KS-ONE-FIFTY-TWO.MIT.EDU [18.235.1.152]) (authenticated bits=0) (User authenticated as mukkala@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFmVg9028116 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 10:48:40 -0500 (EST) Message-Id: <6.2.1.2.2.20051130103802.01ec26e8@po12.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.1.2 Date: Wed, 30 Nov 2005 10:48:31 -0500 To: 6042-probs@theory.csail.mit.edu From: Praveen Pamidimukkala Subject: [Sayan] Week 13 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1114 Content-Length: 403 X-Keywords: NotJunk In section 3.4 of the Notes, the first sentence reads, "Of the more complex distributions, the binomial distribution is surely the most important in computer science." I understand that "an enormous number of analyses in computer science come down to proving that the tails of the binomial and similar distributions are very small," but what is an example of this? Thanks, Praveen Pamidimukkala From mracich@MIT.EDU Wed Nov 30 10:49:55 2005 Return-Path: Received: from grand-central-station.mit.edu (GRAND-CENTRAL-STATION.MIT.EDU [18.7.21.82]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFnt5o008144 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:49:55 -0500 Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by grand-central-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFnn1C010248 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:49:49 -0500 (EST) Received: from MACGREGOR-TWO-FORTY-THREE.MIT.EDU (MACGREGOR-TWO-FORTY-THREE.MIT.EDU [18.239.5.243]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAUFnfMu017323 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:49:42 -0500 (EST) Subject: [Sayan] Comments for Course Notes, Week 13 (Random Variables, Distributions, and Expectation) From: Moira Racich To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Wed, 30 Nov 2005 10:49:40 -0500 Message-Id: <1133365780.7903.6.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.4.1 Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1115 Content-Length: 151 X-Keywords: NotJunk I found section 3, "Probability Distributions", (starting on page 6) confusing. I would appreciate it if this was explained further. Moira Racich From xiaoranz@MIT.EDU Wed Nov 30 10:54:07 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFs75o014625 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:54:07 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFs5rd015441 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:54:06 -0500 (EST) Received: from quickstation-lobby-16-1.mit.edu (QUICKSTATION-LOBBY-16-1.MIT.EDU [18.55.1.64]) (authenticated bits=56) (User authenticated as xiaoranz@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFrxwd000823 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 10:53:59 -0500 (EST) Received: (from xiaoranz@localhost) by quickstation-lobby-16-1.mit.edu (8.12.9) id jAUFrxLj022350; Wed, 30 Nov 2005 10:53:59 -0500 Subject: [Hanson] Week 13 Comments From: Xiaoran Zhang To: 6042-probs@theory.lcs.MIT.EDU Content-Type: text/plain Content-Transfer-Encoding: 7bit Date: Wed, 30 Nov 2005 10:53:58 -0500 Message-Id: <1133366038.22264.2.camel@quickstation-lobby-16-1.mit.edu> Mime-Version: 1.0 X-Mailer: Evolution 2.0.4 X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1116 Content-Length: 190 X-Keywords: NonJunk NotJunk The Birthday principle on page 4-5 is very surprising. The confidence levels is interesting in that it provides a good way to determine the accuracy of the estimations made. Xiaoran Zhang From vbrobbey@MIT.EDU Wed Nov 30 10:54:39 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFsc5o015418 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 10:54:38 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFsbrd016088 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 10:54:37 -0500 (EST) Received: from napoleon (NAPOLEON-BONAPARTE.MIT.EDU [18.18.3.59]) (authenticated bits=0) (User authenticated as vbrobbey@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFsTQm001057 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 10:54:30 -0500 (EST) Message-ID: <003901c5f5c6$587d65f0$3b031212@napoleon> From: "Valery Kwasi Brobbey" To: <6042-probs@theory.csail.mit.edu> Subject: [TA-name] Week 13 Comments Date: Wed, 30 Nov 2005 10:54:27 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0036_01C5F59C.6EA83D70" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 X-Spam-Score: -1.08 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1117 Content-Length: 1208 X-Keywords: NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_0036_01C5F59C.6EA83D70 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Statement 8 on the last tutor problem tricked me. In addition to that I = didn't quite get the winning stategy for the numbers game. Aren't the = numbers that the other guy puts in the envelope completely independent = of the number x that I guess? ------=_NextPart_000_0036_01C5F59C.6EA83D70 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Statement 8 on the last tutor = problem tricked=20 me. In addition to that I didn't quite get the winning stategy for the = numbers=20 game. Aren't the numbers that the other guy puts in the envelope = completely=20 independent of the number x that I = guess?
------=_NextPart_000_0036_01C5F59C.6EA83D70-- From antonk@MIT.EDU Wed Nov 30 10:55:58 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUFtw5o017072 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:55:58 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUFtvrd017604 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:55:57 -0500 (EST) Received: from silencer (SILUET.MIT.EDU [18.234.0.112]) (authenticated bits=0) (User authenticated as antonk@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUFtoDu001683 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 10:55:51 -0500 (EST) From: "Anton Katz" To: <6042-probs@theory.lcs.mit.edu> Subject: [david] discussed more fully Date: Wed, 30 Nov 2005 10:55:46 -0500 Organization: Massachusetts Institute of Technology Message-ID: <005801c5f5c6$87855880$0100a8c0@silencer> MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0059_01C5F59C.9EAF5080" X-Mailer: Microsoft Office Outlook 11 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcX1xobQxfEujCPYTnKW7uj3P5LTGQ== X-Spam-Score: 0.388 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1118 Content-Length: 3304 X-Keywords: NonJunk NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_0059_01C5F59C.9EAF5080 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Hi, Is it possible to discuss the differences between 2 approximations? : Binominal density function Cumulative Binominal distribution function. Thank you, Anton. ------=_NextPart_000_0059_01C5F59C.9EAF5080 Content-Type: text/html; charset="us-ascii" Content-Transfer-Encoding: quoted-printable

Hi,

Is it possible to discuss the differences between 2 = approximations?  :

Binominal density = function

Cumulative Binominal distribution = function.

 

Thank you,

 

Anton.

 

------=_NextPart_000_0059_01C5F59C.9EAF5080-- From jeffhoff@MIT.EDU Wed Nov 30 11:19:10 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUGJA5o004459 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 11:19:10 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUGIPUs013110 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 11:19:09 -0500 (EST) Received: from JERSEY.mit.edu (JERSEY.MIT.EDU [18.235.0.193]) (authenticated bits=0) (User authenticated as jeffhoff@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUG6d1w007090 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 11:06:40 -0500 (EST) Message-Id: <6.2.3.4.2.20051130110528.040ef808@hesiod> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Wed, 30 Nov 2005 11:06:38 -0500 To: 6042-probs@theory.csail.mit.edu From: "Jeffrey D. Hoff" Subject: [Hanson] Week 13 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1119 Content-Length: 123 X-Keywords: NonJunk NotJunk Section 3.4 I found the binomial distribution a little confusing in general. could there be an extension done on this? From crowell@MIT.EDU Wed Nov 30 11:21:35 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUGLZ5o005765 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 11:21:35 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUGLXU2018157 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 11:21:34 -0500 (EST) Received: from [18.238.6.42] (EASTCAMPUS-EIGHT-O-NINE.MIT.EDU [18.238.6.42]) (authenticated bits=0) (User authenticated as crowell@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUGLPBc014376 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 11:21:27 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v734) Content-Transfer-Encoding: 7bit Message-Id: <2A947BFA-FB4C-4B1A-AE4A-25A9751C18C4@mit.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Robert Crowell Subject: [Hanson] Reading Comments Date: Wed, 30 Nov 2005 11:21:26 -0500 X-Mailer: Apple Mail (2.734) X-Spam-Score: 3.076 X-Spam-Level: *** (3.076) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1120 Content-Length: 178 X-Keywords: NotJunk I would like to see more about Expected Value in lecture (this is section 5.2 on page 20). I had some trouble on the tutor problem dealing with this subject. --Rob Crowell From hmzhou@blackbird.csail.mit.edu Wed Nov 30 11:37:42 2005 Return-Path: Received: from blackbird.csail.mit.edu (blackbird.csail.mit.edu [128.30.51.72]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUGbg5o008222; Wed, 30 Nov 2005 11:37:42 -0500 Received: from blackbird.csail.mit.edu (localhost.localdomain [127.0.0.1]) by blackbird.csail.mit.edu (8.13.4/8.13.4) with ESMTP id jAUGbgV0015991; Wed, 30 Nov 2005 11:37:42 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jAUGbg9J015988; Wed, 30 Nov 2005 11:37:42 -0500 Date: Wed, 30 Nov 2005 11:37:42 -0500 (EST) From: Hanson Zhou To: Rebecca Idell cc: 6042-probs@theory.csail.MIT.EDU Subject: Re: reading 13, ta: hanson In-Reply-To: <20051129224640.81zt0eycgv0kkwww@webmail.mit.edu> Message-ID: References: <20051129224640.81zt0eycgv0kkwww@webmail.mit.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1121 Content-Length: 474 X-Keywords: NotJunk Well, most simply: PDF(x) = Pr[R=x]. R is the random variable and PDF(x) asks for the probability that the value of R turns out to be x. -Hanson On Tue, 29 Nov 2005, Rebecca Idell wrote: > > Can you explain more about the probability density function on page 6? > > Rebecca Idell > > -- > Rebecca Idell > Massachusetts Institute of Technology > Electrical Engineering and Computer Science, Class of 2007 > > 479 Commonwealth Avenue > Boston, MA 02215 > (617) 875-0889 > From kktyan@MIT.EDU Wed Nov 30 11:42:56 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUGgu5o009218 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 11:42:56 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUGgtU2018202 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 11:42:55 -0500 (EST) Received: from w92-130-webmail-5.mit.edu (W92-130-WEBMAIL-5.MIT.EDU [18.7.22.136]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUGgmof025128 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 11:42:48 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-5.mit.edu (8.12.4) id jAUGgmMV004734; Wed, 30 Nov 2005 11:42:48 -0500 Received: from BURTON-FOUR-TWENTY-THREE.MIT.EDU (BURTON-FOUR-TWENTY-THREE.MIT.EDU [18.247.6.168]) (User authenticated as kktyan@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 11:42:48 -0500 Message-ID: <20051130114248.jbxdzc9hm2n4kok4@webmail.mit.edu> Date: Wed, 30 Nov 2005 11:42:48 -0500 From: Karena Tyan To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] (Belated) Reading Comments 13 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1122 Content-Length: 610 X-Keywords: NotJunk I apologize for the late reading comments - I nearly forgot to do them, and only just realized that I hadn't done them last night as I'd meant to. In this reading, I was confused by the "Expected Value" sections (starting on page 18). I wasn't sure exactly how one could compute/calculate the expected value, or what the expected value really was, but then I reread the definition of the expected value and figured it out. For the most part, I understood the rest of the reading, though; only the section on expected values was confusing. - Karena -- 410 Memorial Drive Cambridge, MA 02139 (585)957-5923 From hmzhou@blackbird.csail.mit.edu Wed Nov 30 11:45:29 2005 Return-Path: Received: from blackbird.csail.mit.edu (blackbird.csail.mit.edu [128.30.51.72]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUGjT5o009492; Wed, 30 Nov 2005 11:45:29 -0500 Received: from blackbird.csail.mit.edu (localhost.localdomain [127.0.0.1]) by blackbird.csail.mit.edu (8.13.4/8.13.4) with ESMTP id jAUGjTDL016066; Wed, 30 Nov 2005 11:45:29 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jAUGjTI5016063; Wed, 30 Nov 2005 11:45:29 -0500 Date: Wed, 30 Nov 2005 11:45:29 -0500 (EST) From: Hanson Zhou To: Elizabeth Reid cc: 6042-probs@theory.lcs.mit.edu Subject: Re: [Hanson] Reading comments In-Reply-To: <49EAF327-2A3E-4CBD-8256-5E5E11D9E729@MIT.EDU> Message-ID: References: <49EAF327-2A3E-4CBD-8256-5E5E11D9E729@MIT.EDU> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1123 Content-Length: 563 X-Keywords: NotJunk Hi...I'm pretty sure I forwarded your email last week to Prof. Meyer, though you might want to check. -Hanson On Wed, 30 Nov 2005, Elizabeth Reid wrote: > I was initially surprised (and skeptical) about the numbers game > strategy, but its proof makes sense. I guess my only question would > be how to pick the "x" you hope is between L and H, but that's just a > matter of personal opinion. :) > > Oh, and did you get my reading comments last week? You never > responded, and the 6042-probs list was acting oddly when I tried to > email it... > > Elizabeth > From hmzhou@blackbird.csail.mit.edu Wed Nov 30 11:50:56 2005 Return-Path: Received: from blackbird.csail.mit.edu (blackbird.csail.mit.edu [128.30.51.72]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUGou5o010283; Wed, 30 Nov 2005 11:50:56 -0500 Received: from blackbird.csail.mit.edu (localhost.localdomain [127.0.0.1]) by blackbird.csail.mit.edu (8.13.4/8.13.4) with ESMTP id jAUGouMf016122; Wed, 30 Nov 2005 11:50:56 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jAUGouXj016119; Wed, 30 Nov 2005 11:50:56 -0500 Date: Wed, 30 Nov 2005 11:50:56 -0500 (EST) From: Hanson Zhou To: Zachary Adam Ozer cc: 6042-probs@theory.lcs.mit.edu Subject: Re: Tutor Comments: Mean time to failure LN 13 Pg 20 In-Reply-To: <4f2613e50511292146q8dc62b7k4b5f45927a009b6f@mail.gmail.com> Message-ID: References: <4f2613e50511292146q8dc62b7k4b5f45927a009b6f@mail.gmail.com> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1124 Content-Length: 932 X-Keywords: NotJunk I'm not sure I understand your question. If you have an identical backup system that turns on when the first one fails then the mean time to failure would seem to be 1/f + 1/f, where f is the failure probability of each system. -Hanson On Wed, 30 Nov 2005, Zachary Adam Ozer wrote: > I was just wondering how mean time to failure is affected by redundant > systems, ie, what if I have 2 systems where one kicks in when the > other fails. It seems like the probability of failure the same, since > I'm still relying on an identical system, yet that doesn't make sense > from a practical standpoint, since then there'd be little advantage to > using redundant systems. Are they mulitiplicative? IE if the mean > proabaility of failure of one system is 1/100, does the redundancy > cause a mean probability of failure of (1/100)(1/100)? What about as > the redundancy tends towards infinity? > > Just some thoughts, > > -zozer > > From hmzhou@blackbird.csail.mit.edu Wed Nov 30 11:57:55 2005 Return-Path: Received: from blackbird.csail.mit.edu (blackbird.csail.mit.edu [128.30.51.72]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUGvt5o013804; Wed, 30 Nov 2005 11:57:55 -0500 Received: from blackbird.csail.mit.edu (localhost.localdomain [127.0.0.1]) by blackbird.csail.mit.edu (8.13.4/8.13.4) with ESMTP id jAUGvtxb016186; Wed, 30 Nov 2005 11:57:55 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jAUGvtRC016182; Wed, 30 Nov 2005 11:57:55 -0500 Date: Wed, 30 Nov 2005 11:57:55 -0500 (EST) From: Hanson Zhou To: Valery Kwasi Brobbey cc: 6042-probs@theory.csail.mit.edu Subject: Re: [TA-name] Week 13 Comments In-Reply-To: <003901c5f5c6$587d65f0$3b031212@napoleon> Message-ID: References: <003901c5f5c6$587d65f0$3b031212@napoleon> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1125 Content-Length: 625 X-Keywords: NotJunk Hi Valery...by TA-name you mean Hanson :). As for the winning strategy, it is the very fact that your selection of x is random that thwarts anything your opponent might do. So yes, your selection of x is independent, and this actually ends up helping you to do better than 50%. See me if this remains confusing. -Hanson On Wed, 30 Nov 2005, Valery Kwasi Brobbey wrote: > Statement 8 on the last tutor problem tricked me. In addition to that I > didn't quite get the winning stategy for the numbers game. Aren't the > numbers that the other guy puts in the envelope completely independent > of the number x that I guess? From ryan786@MIT.EDU Wed Nov 30 12:44:11 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUHiB5o031754 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 12:44:11 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUHi9U2000813 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 12:44:09 -0500 (EST) Received: from w92-130-webmail-2.mit.edu (W92-130-WEBMAIL-2.MIT.EDU [18.7.22.132]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUHi6MV021483 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 12:44:07 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jAUHi6Je032199; Wed, 30 Nov 2005 12:44:06 -0500 Received: from PSK-SIXTEEN.MIT.EDU (PSK-SIXTEEN.MIT.EDU [18.217.1.16]) (User authenticated as ryan786@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 30 Nov 2005 12:44:06 -0500 Message-ID: <20051130124406.svxufkihkww0s000@webmail.mit.edu> Date: Wed, 30 Nov 2005 12:44:06 -0500 From: Ryan Young Reply-to: ryoung@MIT.EDU To: 6042-probs@theory.lcs.MIT.EDU Subject: [sayan] 13 reading MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1126 Content-Length: 252 X-Keywords: NonJunk NotJunk Apologies again for the late email, I have just now been able to read the pdf. The most difficult parts were the Probability Distributions (Section 3). I do think class today will clear it up though, as that is the topic of lecture (I think). -Ryan From mitras@theory.csail.mit.edu Wed Nov 30 13:06:42 2005 Return-Path: Received: from grand-central-station.mit.edu (GRAND-CENTRAL-STATION.MIT.EDU [18.7.21.82]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUI6g5o006143 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 13:06:42 -0500 Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by grand-central-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUI6evv017399; Wed, 30 Nov 2005 13:06:40 -0500 (EST) Received: from [128.30.51.97] (drake.csail.mit.edu [128.30.51.97]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAUI6Wok016852; Wed, 30 Nov 2005 13:06:32 -0500 (EST) Message-ID: <438DEA25.1040205@theory.csail.mit.edu> Date: Wed, 30 Nov 2005 13:06:29 -0500 From: Sayan Mitra User-Agent: Mozilla Thunderbird 1.0.7-1.1.fc3 (X11/20050929) X-Accept-Language: en-us, en MIME-Version: 1.0 To: "David A. Nedzel" CC: 6042-probs@theory.lcs.mit.edu Subject: Re: [Sayan] Week 13 Comments References: <438CE7F6.8000506@mit.edu> In-Reply-To: <438CE7F6.8000506@mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1127 Content-Length: 314 X-Keywords: NotJunk Expectation will be covered on Friday, and variance on next Wednesday. Best, sayan David A. Nedzel wrote: > I'm fairly comfortable with this material, I've seen most of it in > 6.041. It might be nice to have a refresher during lecture on the > expectation & variance of different distributions. > > - David From mitras@theory.csail.mit.edu Wed Nov 30 13:08:26 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUI8Q5o006452 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 13:08:26 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAUI8PEu003533 for <6042-probs@theory.csail.mit.edu>; Wed, 30 Nov 2005 13:08:25 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUI3VnT000063; Wed, 30 Nov 2005 13:03:31 -0500 (EST) Received: from [128.30.51.97] (drake.csail.mit.edu [128.30.51.97]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAUI3Sok016662; Wed, 30 Nov 2005 13:03:29 -0500 (EST) Message-ID: <438DE970.7030309@theory.csail.mit.edu> Date: Wed, 30 Nov 2005 13:03:28 -0500 From: Sayan Mitra User-Agent: Mozilla Thunderbird 1.0.7-1.1.fc3 (X11/20050929) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Praveen Pamidimukkala CC: 6042-probs@theory.csail.mit.edu Subject: Re: [Sayan] Week 12 Comments References: <6.2.1.2.2.20051128140633.03e5fa00@po12.mit.edu> In-Reply-To: <6.2.1.2.2.20051128140633.03e5fa00@po12.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1128 Content-Length: 677 X-Keywords: NotJunk Events are sets of points in the sample space. Events are disjoint when these sets are disjoint. E.g, consider a 6-sided dice roll experiment. Define Event 1, A = even number comes up, B = odd number, C = prime number. Then, A and B are disjoint, A and C are not. -sayan Praveen Pamidimukkala wrote: > In section 4.3 of the Course Notes on Probability, disjointness is > mentioned in comparison to independence. I understand that > mathematically, when two events are disjoint, Pr{AintB} = 0 as opposed > to Pr{AintB} = Pr{A} x Pr{B}, which applies for independence. > However, in terms of events, how could this be described? > > Thanks, > Praveen Pamidimukkala > From mitras@theory.csail.mit.edu Wed Nov 30 13:20:15 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUIKF5o024388 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 13:20:15 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAUIKEEu024893 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 13:20:14 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUIKDnT000919; Wed, 30 Nov 2005 13:20:13 -0500 (EST) Received: from [128.30.51.97] (drake.csail.mit.edu [128.30.51.97]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAUIK6ok017762; Wed, 30 Nov 2005 13:20:07 -0500 (EST) Message-ID: <438DED56.60101@theory.csail.mit.edu> Date: Wed, 30 Nov 2005 13:20:06 -0500 From: Sayan Mitra User-Agent: Mozilla Thunderbird 1.0.7-1.1.fc3 (X11/20050929) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Moira Racich CC: 6042-probs@theory.lcs.mit.edu Subject: Re: [Sayan] Comments for Course Notes, Week 13 (Random Variables, Distributions, and Expectation) References: <1133365780.7903.6.camel@localhost.localdomain> In-Reply-To: <1133365780.7903.6.camel@localhost.localdomain> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1129 Content-Length: 236 X-Keywords: NotJunk Hope today's lecture is going to help. Best, Sayan Moira Racich wrote: >I found section 3, "Probability Distributions", (starting on page 6) >confusing. I would appreciate it if this was explained further. > >Moira Racich > > > From meyer@imap.theory.csail.mit.edu Wed Nov 30 11:45:30 2005 Return-Path: Received: from grand-central-station.mit.edu (GRAND-CENTRAL-STATION.MIT.EDU [18.7.21.82]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUGjS5o009479 for <6042-staff@theory.csail.mit.edu>; Wed, 30 Nov 2005 11:45:28 -0500 Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by grand-central-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUGjSvv013275; Wed, 30 Nov 2005 11:45:28 -0500 (EST) Received: from [128.30.51.97] (drake.csail.mit.edu [128.30.51.97]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAUGjOMu021156; Wed, 30 Nov 2005 11:45:24 -0500 (EST) Message-ID: <438DD722.3020304@theory.csail.mit.edu> Date: Wed, 30 Nov 2005 11:45:22 -0500 From: Sayan Mitra User-Agent: Mozilla Thunderbird 1.0.7-1.1.fc3 (X11/20050929) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Jesus Medrano , 6042 staff <6042-staff@theory.csail.mit.edu> Subject: Re: [sayan] probability References: <1133329953.10283.2.camel@localhost> In-Reply-To: <1133329953.10283.2.camel@localhost> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: -2.599 X-Scanned-By: MIMEDefang 2.42 X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on theory.csail.mit.edu X-Spam-Level: X-Spam-Status: No, hits=-4.9 required=3.7 tests=AWL,BAYES_00 autolearn=ham version=2.63 Status: RO Content-Length: 765 X-UID: 1130 X-Keywords: NotJunk Hi, You have to be careful about phrasing these polling related probabilistic claims. The sample size of 600 is derived for a particular accuracy (0.04) and for a particular probability of error (5%). The surprising thing is that, the sample size required is independent of the actual size of the population. We'll do a similar problem in class today, hopefully it will clear up these ideas. Best, Sayan Jesus Medrano wrote: >I'm still uncertain about the theorem in the notes about the binomial >sampling. What does this mean? Is it true that only 600 people are >needed to be sampled out of any size n population to get an accurate >view of the entire population. This does not seem very reasonable? Is >this done in practice? > >Jesus Medrano > > From meyer@imap.theory.csail.mit.edu Wed Nov 30 02:01:47 2005 Message-ID: <438D4E61.5070509@csail.mit.edu> Date: Wed, 30 Nov 2005 02:01:53 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Yaser Khan Subject: Re: David: tp13 reading comments References: <200511300621.jAU6LNe5029473@outgoing.mit.edu> In-Reply-To: <200511300621.jAU6LNe5029473@outgoing.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 474 X-UID: 1131 X-Keywords: poisson might get mentioned VERY briefly in the last week. no t or chi. regards, A. Yaser Khan wrote: > Hi David, > > > > As a whole, the reading was a bit dense with formulas, to the extent > that I keep getting similar definitions mixed up (for instance the > distinctions between the distributions). However, my question is: will > we be concerned with the t, poisson, or chi distributions in terms of > random variables? > > > Thanks! > > > > _Yaser > From dshin@MIT.EDU Wed Nov 30 14:09:03 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUJ935o022795 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 14:09:03 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAUJ92WT014770 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 14:09:02 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUJ926j003465; Wed, 30 Nov 2005 14:09:02 -0500 (EST) Received: from [192.168.1.5] (c-65-96-190-64.hsd1.ma.comcast.net [65.96.190.64]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAUJ8sok020901; Wed, 30 Nov 2005 14:08:54 -0500 (EST) Message-ID: <438DF8C0.9020501@mit.edu> Date: Wed, 30 Nov 2005 14:08:48 -0500 From: David Shin User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Katherine Romer CC: 6042-probs@theory.lcs.MIT.EDU Subject: Re: [David] Email comments for reading References: <1133362273.32582.2.camel@m56-129-21.mit.edu> In-Reply-To: <1133362273.32582.2.camel@m56-129-21.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 3.631 X-Spam-Level: *** (3.631) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1132 Content-Length: 542 X-Keywords: NotJunk Yes, that is correct. Another way to see it is to define an indicator variable G(x) for each baby x that equals 1 if x is a girl and 0 if x is a boy. Every baby x has E[G(x)] = 0.5, so by linearity of expectation the expected value of SUM(G(x)) is 0.5*population. DS Katherine Romer wrote: >p.21 "If every couple follows the strategy of having children until they >get a girl, what will eventually happen to the fraction of girls born in >this world?" >Will it remain the same (because each couple expects to have 2 >children)? > > From mdmurray@MIT.EDU Wed Nov 30 14:19:06 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAUJJ55o027440 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 14:19:05 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAUJJ4Wx022899 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 14:19:04 -0500 (EST) Received: from w20-575-15.mit.edu (W20-575-15.MIT.EDU [18.187.0.34]) (authenticated bits=56) (User authenticated as mdmurray@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAUJIu2w000931 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.MIT.EDU>; Wed, 30 Nov 2005 14:18:57 -0500 (EST) Received: (from mdmurray@localhost) by w20-575-15.mit.edu (8.12.9) id jAUJIuZK012066; Wed, 30 Nov 2005 14:18:56 -0500 Date: Wed, 30 Nov 2005 14:18:56 -0500 (EST) From: Michael D Murray To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] Reading question Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1133 Content-Length: 279 X-Keywords: NotJunk Hey, Sorry for the delay, the reading was quite long to be done in two days. I am curious about the Bernoulli Distribution, do we need to know it in detail? There isn't alot of information in 3.1 and I don't really understand what the point of it is. Thanks, Michael Murray From shreyes19@gmail.com Wed Nov 30 19:34:38 2005 Return-Path: Received: from nproxy.gmail.com (nproxy.gmail.com [64.233.182.198]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jB10Yb5o021450 for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 19:34:38 -0500 Received: by nproxy.gmail.com with SMTP id g2so49912nfe for <6042-probs@theory.lcs.mit.edu>; Wed, 30 Nov 2005 16:34:37 -0800 (PST) DomainKey-Signature: a=rsa-sha1; q=dns; c=nofws; s=beta; d=gmail.com; h=received:message-id:date:from:sender:to:subject:mime-version:content-type; b=Mf8FlvaaN9781ED5bv0lmLml1BUBTOk52nPho1zfDy02zwk3dWbtWn1UxULEZicfvL9C4u1QxDLPXQBIgopKU4p247PaIEurdu8IO06E40840KZFHU4TeF8JRCsi6dEPu2/DpVxYGuQqtmcghgBHQUBKaQHo+ZzxTLHnGEQBnaY= Received: by 10.48.238.12 with SMTP id l12mr111979nfh; Wed, 30 Nov 2005 16:34:37 -0800 (PST) Received: by 10.48.161.8 with HTTP; Wed, 30 Nov 2005 16:34:37 -0800 (PST) Message-ID: <3c33fe380511301634q4d61bc5eo1cab3a2cc984f6e8@mail.gmail.com> Date: Wed, 30 Nov 2005 19:34:37 -0500 From: Shreyes Seshasai Sender: shreyes19@gmail.com To: 6042-probs@theory.lcs.mit.edu Subject: [Sayan] Week 13 Reading Comments MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_3830_21133891.1133397277067" Status: RO X-UID: 1134 Content-Length: 2210 X-Keywords: NotJunk ------=_Part_3830_21133891.1133397277067 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Hi, Here are my comments on week 13's reading comments: My question deals with the the definition of Independence presented in the notes. The notes state on page 3: Random variables R1 and R2 are independent if for all x1 in the codomain of R1, and x2 in the codomain of R2, we have: Pr {R1 =3D x1 | R2 =3D x2} =3D Pr {R1 =3D x1} =B7 Pr {R2 =3D x2} . This definition makes sense to me, but my questions is whether knowing this is true implies Independence. From other classes (6.041), we are able to prove Independence by showing how the above equation holds, but there are some questions where the equation holds but intuitively R1 and R2 are not independent. I can't think of an example off the top of my head, but i kno= w for other formulas describing Independence (like E[XY] =3D E[X]E[Y]), provi= ng the equation does not necessarily prove Independence. Thanks, Shreyes group 7 ------=_Part_3830_21133891.1133397277067 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Hi,

Here are my comments on week 13's reading comments:

My question deals with the the definition of Independence presented in the = notes.  The notes state on page 3:
Random variables R1 and R2 are independent if for all x1 in the codomain of= R1, and x2 in the
codomain of R2, we have:
Pr {R1 =3D x1 | R2 =3D x2} =3D Pr {R1 =3D x1} =B7 Pr {R2 =3D x2} .
This definition makes sense to me, but my questions is whether knowing this is true implies Independence.  From other classes (6.041), we are able to prove Independence by showing how the above equation holds, but there are some questions where the equation holds but intuitively R1 and R2 are not independent.  I can't think of an example off the top of my head, but i know for other formulas describing Independence (like E[XY] =3D E[X]E[Y]), proving the equation does not necessarily prove Independence.

Thanks,
Shreyes
group 7
------=_Part_3830_21133891.1133397277067-- From mitras@theory.csail.mit.edu Thu Dec 1 17:28:19 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jB1MSIXl016741 for <6042-probs@theory.lcs.mit.edu>; Thu, 1 Dec 2005 17:28:19 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jB1MSHKQ022767; Thu, 1 Dec 2005 17:28:17 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jB1MSHlA012477; Thu, 1 Dec 2005 17:28:17 -0500 (EST) Received: from [128.30.51.97] (drake.csail.mit.edu [128.30.51.97]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jB1MSDMu003838; Thu, 1 Dec 2005 17:28:13 -0500 (EST) Message-ID: <438F78FD.6080208@theory.csail.mit.edu> Date: Thu, 01 Dec 2005 17:28:13 -0500 From: Sayan Mitra User-Agent: Mozilla Thunderbird 1.0.7-1.1.fc3 (X11/20050929) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Shreyes Seshasai CC: 6042-probs@theory.lcs.mit.edu Subject: Re: [Sayan] Week 13 Reading Comments References: <3c33fe380511301634q4d61bc5eo1cab3a2cc984f6e8@mail.gmail.com> In-Reply-To: <3c33fe380511301634q4d61bc5eo1cab3a2cc984f6e8@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 8bit X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1135 Content-Length: 1972 X-Keywords: NotJunk Good question. A. X and Y are independent if and only if (<=>) P(X =x, Y = y) = for all x, y, P(X=x)P(Y=y). This is the definition of independence. B. X and Y are independent => E[XY] = E[X] E[Y], this is a one way implication. Here's a quick proof: E[XY] = \sum_{i,j} a_i b_j P[X = a_i, Y = b_j] = \sum_{i,j} a_i P[ X = a_i] b_j P[Y = b_j], since X and Y are independent. = \sum_i a_i P[X =a_i] \sum_j b_j P[Y = b_j] = E[X]E[Y] But the converse is not necessarily true, i.e., E[XY] = E[X]E[Y] does not imply independence of X Y. Here's an example: Let (X, Y) assume values (1,0), (0,1), (-1,0), and (0,-1) with equal probabilities 1/4. Then E[X] = E[Y] = 1 * 1/4 + (-1) * 1/4 = 0. E[XY] = 0. So, we do have E[XY] =E[X]E[Y]. Now lets see if they are independent. Choose x = 0, y = 0. P(X=0) = P(Y =0) = 1/2 whereas P(X=0, Y=0) = 0. So, P(X = 0, Y=0) is not = P(X=0)P(Y=0), i.e., they are not independent. But remember, E[X+Y] = E[X] + E[Y] regardless of independence. Best, Sayan Shreyes Seshasai wrote: > Hi, > > Here are my comments on week 13's reading comments: > > My question deals with the the definition of Independence presented in > the notes. The notes state on page 3: > Random variables R1 and R2 are independent if for all x1 in the > codomain of R1, and x2 in the > codomain of R2, we have: > Pr {R1 = x1 | R2 = x2} = Pr {R1 = x1} · Pr {R2 = x2} . > This definition makes sense to me, but my questions is whether knowing > this is true implies Independence. From other classes (6.041), we are > able to prove Independence by showing how the above equation holds, > but there are some questions where the equation holds but intuitively > R1 and R2 are not independent. I can't think of an example off the > top of my head, but i know for other formulas describing Independence > (like E[XY] = E[X]E[Y]), proving the equation does not necessarily > prove Independence. > > Thanks, > Shreyes > group 7 From dangut@MIT.EDU Thu Dec 1 19:39:06 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jB20d6Iu009822 for <6042-probs@theory.csail.MIT.EDU>; Thu, 1 Dec 2005 19:39:06 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jB20d5Gi015781 for <6042-probs@theory.csail.MIT.EDU>; Thu, 1 Dec 2005 19:39:05 -0500 (EST) Received: from w92-130-webmail-2.mit.edu (W92-130-WEBMAIL-2.MIT.EDU [18.7.22.132]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB20d3S7004750 for <6042-probs@theory.csail.MIT.EDU>; Thu, 1 Dec 2005 19:39:04 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jB20d308019284; Thu, 1 Dec 2005 19:39:03 -0500 Received: from MACGREGOR-THREE-TWENTY-NINE.MIT.EDU (MACGREGOR-THREE-TWENTY-NINE.MIT.EDU [18.239.6.74]) (User authenticated as dangut@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Thu, 1 Dec 2005 19:39:03 -0500 Message-ID: <20051201193903.i5g5e2m91nogg04w@webmail.mit.edu> Date: Thu, 1 Dec 2005 19:39:03 -0500 From: Daniel A Gutierrez To: 6042-probs@theory.csail.MIT.EDU Subject: [Hansen] TP13 Reading Response MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1136 Content-Length: 87 X-Keywords: NotJunk I'm still comfortable with the material, I think the birthday example was pretty cool.