From juang@MIT.EDU Sat Dec 3 23:07:57 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 jB447v6N000595 for <6042-probs@theory.lcs.mit.edu>; Sat, 3 Dec 2005 23:07:57 -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 jB447tCH021544 for <6042-probs@theory.lcs.mit.edu>; Sat, 3 Dec 2005 23:07:55 -0500 (EST) Received: from [18.238.6.17] (EASTCAMPUS-SEVEN-EIGHTY-FOUR.MIT.EDU [18.238.6.17]) (authenticated bits=0) (User authenticated as juang@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB447nWj021592 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Sat, 3 Dec 2005 23:07:49 -0500 (EST) Message-ID: <43926B8E.9080106@mit.edu> Date: Sat, 03 Dec 2005 23:07:42 -0500 From: Jason Juang User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.5) Gecko/20041201 Thunderbird/1.0RC1 Mnenhy/0.6.0.104 X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [David] Week 14 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 X-IMAPbase: 1126748715 1231 NonJunk $Label4 $Label1 $Label2 $Label3 $Label5 Junk $MDNSent $Forwarded NotJunk Status: RO X-UID: 1137 Content-Length: 331 X-Keywords: NonJunk NotJunk I don't have much comment on the reading, so I'll instead mention that Problem B4 on the Putnam today was, paraphrased: Let f(m,n) be the number of n-tuples of integers (x_1, x_2, ..., x_n) which satisfy |x_1| + |x_2| + ... + |x_n| <= m. Show that f(m,n) = f(n,m). ... Sounds like a good final exam question to me ;) Jason. From kevin08@MIT.EDU Sun Dec 4 05:29:38 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 jB4ATc6N011798 for <6042-probs@theory.lcs.mit.edu>; Sun, 4 Dec 2005 05:29:38 -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 jB4ATbwU018983 for <6042-probs@theory.lcs.mit.edu>; Sun, 4 Dec 2005 05:29:37 -0500 (EST) Received: from kevlar.mit.edu (NEXT-FIVE-EIGHTY-SIX.MIT.EDU [18.242.7.75]) (authenticated bits=0) (User authenticated as kevin08@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB4ATXsV012249 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Sun, 4 Dec 2005 05:29:35 -0500 (EST) Message-Id: <6.2.3.4.2.20051204052628.0296b7b8@po10.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Sun, 04 Dec 2005 05:29:34 -0500 To: 6042-probs@theory.lcs.mit.edu From: Kevin Wang Subject: [Hanson] Week's 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: 1138 Content-Length: 236 X-Keywords: NonJunk NotJunk Hi, I had a general question about this week's readings--it seems that Chebyshev's Inequality (S7, Pg. 12) is always tighter than Markov's Inequality (S6, pg. 10). Is there a simple proof of this, or is it even true? Thanks, Kevin From ajshafer@MIT.EDU Sun Dec 4 11:50:07 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 jB4Go76N002555 for <6042-probs@theory.csail.mit.edu>; Sun, 4 Dec 2005 11:50:07 -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 jB4Go6OG017200 for <6042-probs@theory.csail.mit.edu>; Sun, 4 Dec 2005 11:50:06 -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 jB4Gnxfj007857 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Sun, 4 Dec 2005 11:50:00 -0500 (EST) Message-ID: <000201c5f8f2$c4620760$6d04f712@ajshafer> From: "Andrew Shafer" To: <6042-probs@theory.csail.mit.edu> Subject: [Sayan] Week 14 Comments Date: Sun, 4 Dec 2005 11:50:00 -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 X-UID: 1139 Content-Length: 299 X-Keywords: NonJunk NotJunk Will we be required to know the expectation and variance for some standard random variables? -Andrew ---------------------------- Illegitmitatum Non Carborundum Est Andrew Shafer, MIT Blog http://shaferandrew.blogspot.com Si hoc legere scis numium eruditionis habes. ---------------------------- From ksindi@MIT.EDU Sun Dec 4 21:07:43 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 jB527g6N027943 for <6042-probs@theory.csail.MIT.EDU>; Sun, 4 Dec 2005 21:07:42 -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 jB527fss018085 for <6042-probs@theory.csail.MIT.EDU>; Sun, 4 Dec 2005 21:07:41 -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 jB527R8a011532 for <6042-probs@theory.csail.MIT.EDU>; Sun, 4 Dec 2005 21:07:27 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-6.mit.edu (8.12.4) id jB527RsX015403; Sun, 4 Dec 2005 21:07:27 -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 ; Sun, 4 Dec 2005 21:07:27 -0500 Message-ID: <20051204210727.dhabmn2m4bw4wksk@webmail.mit.edu> Date: Sun, 4 Dec 2005 21:07:27 -0500 From: Kamil Y Sindi To: 6042-probs@theory.csail.MIT.EDU Subject: [DAVID] WEEK 14 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: -1.602 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1140 Content-Length: 296 X-Keywords: NotJunk I found everything well explained but still have trouble grasping the qualitative nature of the standard deviation; when to say, for example, "wow that's a high standard deviation!". I'd also like to hear in class, in a bit more detail, about when one can't use the Chebychev inequality. -Kamil From bens@MIT.EDU Mon Dec 5 01:42:24 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 jB56gN6N009230 for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 01:42:23 -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 jB56gMV9015195 for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 01:42:22 -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 jB56gKkr029488 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 01:42:20 -0500 (EST) Message-ID: <4393E13D.2060705@mit.edu> Date: Mon, 05 Dec 2005 01:42:05 -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 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: 1141 Content-Length: 108 X-Keywords: NotJunk The Chebyshev bound is awesome. Are there distributions for which Markov, chebyshev, etc. are always tight? From kjhollen@MIT.EDU Mon Dec 5 03:01:13 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 jB581D6N023388 for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 03:01:13 -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 jB581CK2025291 for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 03:01:12 -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 jB581CI2016221 for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 03:01:12 -0500 (EST) Received: from MACGREGOR-FOUR-SIXTY-EIGHT.MIT.EDU (MACGREGOR-FOUR-SIXTY-EIGHT.MIT.EDU [18.239.6.213]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jB5814Mu021999 for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 03:01:04 -0500 (EST) Subject: [Hanson] confused about calculating variance From: Kate Hollenbach To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Mon, 05 Dec 2005 03:01:02 -0500 Message-Id: <1133769662.8170.2.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.4.1 Content-Transfer-Encoding: 7bit X-Spam-Score: 3.817 X-Spam-Level: *** (3.817) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1142 Content-Length: 372 X-Status: A X-Keywords: NonJunk NotJunk while the gambling game example for calculating variance in the notes was a good illustrating of the concept (p. 13), I found it difficult to apply the concept to the online tutor problem about the variance of the number of heads that appear in 100 coin flips. it might be helpful to explain how to do variance calculations with an example that has more than 2 outcomes. From meyer@imap.theory.csail.mit.edu Mon Dec 05 09:33:26 2005 Message-ID: <43944FBB.4050506@csail.mit.edu> Date: Mon, 05 Dec 2005 09:33:31 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Kate Hollenbach Subject: Re: [Hanson] confused about calculating variance References: <1133769662.8170.2.camel@localhost.localdomain> In-Reply-To: <1133769662.8170.2.camel@localhost.localdomain> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 451 X-UID: 1143 X-Keywords: did you read ln14, sec 1.4? regards, A. Kate Hollenbach wrote: >while the gambling game example for calculating variance in the notes >was a good illustrating of the concept (p. 13), I found it difficult to >apply the concept to the online tutor problem about the variance of the >number of heads that appear in 100 coin flips. it might be helpful to >explain how to do variance calculations with an example that has more >than 2 outcomes. > > > From xiaoranz@MIT.EDU Mon Dec 5 10:48:37 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 jB5Fmb6N029091 for <6042-probs@theory.lcs.MIT.EDU>; Mon, 5 Dec 2005 10:48:37 -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 jB5Fmasu022640 for <6042-probs@theory.lcs.MIT.EDU>; Mon, 5 Dec 2005 10:48:36 -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 jB5FmUQB025497 for <6042-probs@theory.lcs.MIT.EDU>; Mon, 5 Dec 2005 10:48:30 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jB5FmT7h006467; Mon, 5 Dec 2005 10:48:29 -0500 Received: from M56-129-20.MIT.EDU (M56-129-20.MIT.EDU [18.56.0.49]) (User authenticated as xiaoranz@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Mon, 5 Dec 2005 10:48:29 -0500 Message-ID: <20051205104829.h5tkt7zd8m2so0wc@webmail.mit.edu> Date: Mon, 5 Dec 2005 10:48:29 -0500 From: "Xiaoran (Sharon) Zhang" To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] Week 14 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: 1144 Content-Length: 589 X-Keywords: NonJunk NotJunk I thought section 2.1 on expected number of meals to get each Racin' Rocket is an interesting problem and application. Also, The Markov and Chebyshev's Theorems provides good way to upper bound certain probabilities and helpful in checking result. Xiaoran Zhang ************************************************** Xiaoran (Sharon) Zhang Class of 2008 Department of Biology & Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology 320 Memorial Drive, Cambridge, MA 02139 E-mail: xiaoranz@mit.edu ************************************************** From meyer@imap.theory.csail.mit.edu Mon Dec 05 10:32:54 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 jB5FWq6N021682 for ; Mon, 5 Dec 2005 10:32:53 -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 1EjIKi-0003g2-Pz for meyer@csail.MIT.EDU; Mon, 05 Dec 2005 10:32:52 -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 jB5FWpsu003680 for ; Mon, 5 Dec 2005 10:32:51 -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 jB5FWm04018197 for ; Mon, 5 Dec 2005 10:32:48 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-6.mit.edu (8.12.4) id jB5FWmbA017919; Mon, 5 Dec 2005 10:32:48 -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 ; Mon, 5 Dec 2005 10:32:48 -0500 Message-ID: <20051205103248.opf3mjvmlvcw8k0g@webmail.mit.edu> Date: Mon, 5 Dec 2005 10:32:48 -0500 From: Kate Hollenbach To: "Prof. Albert R. Meyer" Subject: Re: [Hanson] confused about calculating variance References: <1133769662.8170.2.camel@localhost.localdomain> <43944FBB.4050506@csail.mit.edu> In-Reply-To: <43944FBB.4050506@csail.mit.edu> MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format="flowed" Content-Disposition: inline User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Scanned-By: MIMEDefang 2.42 Content-Transfer-Encoding: 7bit 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=BAYES_00 autolearn=ham version=2.63 Status: RO X-Status: A Content-Length: 716 X-UID: 1145 X-Keywords: NonJunk NotJunk yes, and it did help me figure out how to find the expectation of the number of heads. but I am still having trouble with translating it into the variance formulas found on p. 13 and 16. Quoting "Prof. Albert R. Meyer" : > did you read ln14, sec 1.4? > regards, A. > > Kate Hollenbach wrote: > >> while the gambling game example for calculating variance in the notes >> was a good illustrating of the concept (p. 13), I found it difficult to >> apply the concept to the online tutor problem about the variance of the >> number of heads that appear in 100 coin flips. it might be helpful to >> explain how to do variance calculations with an example that has more >> than 2 outcomes. >> >> > From hmzhou@blackbird.csail.mit.edu Mon Dec 5 11:15:57 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 jB5GFv6N026964; Mon, 5 Dec 2005 11:15:57 -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 jB5GFvoK030117; Mon, 5 Dec 2005 11:15:57 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jB5GFvnJ030114; Mon, 5 Dec 2005 11:15:57 -0500 Date: Mon, 5 Dec 2005 11:15:56 -0500 (EST) From: Hanson Zhou To: Kevin Wang cc: 6042-probs@theory.lcs.mit.edu Subject: Re: [Hanson] Week's reading comments In-Reply-To: <6.2.3.4.2.20051204052628.0296b7b8@po10.mit.edu> Message-ID: References: <6.2.3.4.2.20051204052628.0296b7b8@po10.mit.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1146 Content-Length: 602 X-Keywords: NotJunk Well...Chebyshev is nothing more than applying Markov's inequality in a certain way as you will see from the proof of it, so I don't think you can say it is stronger. However, typically, if the variance is known to you and small, then you can often do better using that than the usual form of Markov. -Hanson On Sun, 4 Dec 2005, Kevin Wang wrote: > Hi, > > I had a general question about this week's readings--it seems that > Chebyshev's Inequality (S7, Pg. 12) is always tighter than Markov's > Inequality (S6, pg. 10). Is there a simple proof of this, or is it even true? > > Thanks, > Kevin > > From meyer@imap.theory.csail.mit.edu Mon Dec 05 18:34:20 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 jB5NYJ6N001543 for <6042-staff@theory.csail.mit.edu>; Mon, 5 Dec 2005 18:34:19 -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 jB5NYIw2005948 for <6042-staff@theory.csail.mit.edu>; Mon, 5 Dec 2005 18:34:18 -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 jB5NYH9Q027861; Mon, 5 Dec 2005 18:34:17 -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 jB5NYEMu018948; Mon, 5 Dec 2005 18:34:14 -0500 (EST) Message-ID: <4394CE74.1070101@mit.edu> Date: Mon, 05 Dec 2005 18:34:12 -0500 From: David Shin User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Richard Hughes CC: 6042-staff@theory.csail.mit.edu Subject: Re: I can't figure out how to calculate variance References: In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit 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=-4.8 required=3.7 tests=AWL,BAYES_00,RCVD_IN_SORBS autolearn=no version=2.63 Status: RO Content-Length: 702 X-UID: 1147 X-Keywords: NotJunk Richard, You also know that if A and B are independent, then Var(A+B) = Var(A) + Var(B). Or, if A1, A2, ..., A99, A100 are mutually independent, then Var(A1+A2+...+A99+A100) = Var(A1)+Var(A2)+...+Var(A99)+Var(A100). DS Richard Hughes wrote: > Or, I can figure out how, but I can't actually DO it. > > I'm trying to do Tutor Problem 14.3 and it's giving me more trouble > than a tutor problem should. I honest to god cannot figure out how to > calculate the variance on a number of heads. I know the formula is > Var(R) = E[R^2] - E^2[R]. I know that E^2[R] = 2500. I absolutely > cannot figure out how to calculate R^2 or the expected value of it. > HELP ME PLEASE. :-( > > Richard > From meyer@imap.theory.csail.mit.edu Mon Dec 05 18:41:40 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 jB5Nfc6N003971 for <6042-staff@theory.csail.mit.edu>; Mon, 5 Dec 2005 18:41:38 -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 jB5NfaTT000346; Mon, 5 Dec 2005 18:41:36 -0500 (EST) Received: from [18.24.1.16] (24-1-16.dynamic.csail.mit.edu [18.24.1.16]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jB5NfXok006079; Mon, 5 Dec 2005 18:41:34 -0500 (EST) In-Reply-To: <4394CE74.1070101@mit.edu> References: <4394CE74.1070101@mit.edu> Mime-Version: 1.0 (Apple Message framework v623) Content-Type: text/plain; charset=US-ASCII; format=flowed Message-Id: <546ea75c652249fb2cfeb63e00b0c955@mit.edu> Content-Transfer-Encoding: 7bit Cc: 6042-staff@theory.csail.mit.edu From: Richard Hughes Subject: Re: I can't figure out how to calculate variance Date: Mon, 5 Dec 2005 18:41:32 -0500 To: David Shin X-Mailer: Apple Mail (2.623) 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=BAYES_00 autolearn=ham version=2.63 Status: RO Content-Length: 828 X-UID: 1148 X-Keywords: NotJunk Thanks. That did it for me, I solved it. Richard On Dec 5, 2005, at 6:34 PM, David Shin wrote: > Richard, > > You also know that if A and B are independent, then Var(A+B) = Var(A) > + Var(B). > Or, if A1, A2, ..., A99, A100 are mutually independent, then > Var(A1+A2+...+A99+A100) = Var(A1)+Var(A2)+...+Var(A99)+Var(A100). > > DS > > Richard Hughes wrote: > >> Or, I can figure out how, but I can't actually DO it. >> >> I'm trying to do Tutor Problem 14.3 and it's giving me more trouble >> than a tutor problem should. I honest to god cannot figure out how >> to calculate the variance on a number of heads. I know the formula >> is Var(R) = E[R^2] - E^2[R]. I know that E^2[R] = 2500. I >> absolutely cannot figure out how to calculate R^2 or the expected >> value of it. HELP ME PLEASE. :-( >> >> Richard >> From meyer@imap.theory.csail.mit.edu Mon Dec 05 18:41:38 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 jB5Nfc6N003971 for <6042-staff@theory.csail.mit.edu>; Mon, 5 Dec 2005 18:41:38 -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 jB5NfaTT000346; Mon, 5 Dec 2005 18:41:36 -0500 (EST) Received: from [18.24.1.16] (24-1-16.dynamic.csail.mit.edu [18.24.1.16]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jB5NfXok006079; Mon, 5 Dec 2005 18:41:34 -0500 (EST) In-Reply-To: <4394CE74.1070101@mit.edu> References: <4394CE74.1070101@mit.edu> Mime-Version: 1.0 (Apple Message framework v623) Content-Type: text/plain; charset=US-ASCII; format=flowed Message-Id: <546ea75c652249fb2cfeb63e00b0c955@mit.edu> Content-Transfer-Encoding: 7bit Cc: 6042-staff@theory.csail.mit.edu From: Richard Hughes Subject: Re: I can't figure out how to calculate variance Date: Mon, 5 Dec 2005 18:41:32 -0500 To: David Shin 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 Content-Length: 829 X-UID: 1149 X-Keywords: NonJunk NotJunk Thanks. That did it for me, I solved it. Richard On Dec 5, 2005, at 6:34 PM, David Shin wrote: > Richard, > > You also know that if A and B are independent, then Var(A+B) = Var(A) > + Var(B). > Or, if A1, A2, ..., A99, A100 are mutually independent, then > Var(A1+A2+...+A99+A100) = Var(A1)+Var(A2)+...+Var(A99)+Var(A100). > > DS > > Richard Hughes wrote: > >> Or, I can figure out how, but I can't actually DO it. >> >> I'm trying to do Tutor Problem 14.3 and it's giving me more trouble >> than a tutor problem should. I honest to god cannot figure out how >> to calculate the variance on a number of heads. I know the formula >> is Var(R) = E[R^2] - E^2[R]. I know that E^2[R] = 2500. I >> absolutely cannot figure out how to calculate R^2 or the expected >> value of it. HELP ME PLEASE. :-( >> >> Richard >> From cwong08@MIT.EDU Mon Dec 5 20:29:29 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 jB61TT6N009942 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 20:29:29 -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 jB61TSN1007031 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 20:29:28 -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 jB61Rg9L001857 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 20:27:42 -0500 (EST) Received: from [127.0.0.1] (CWONG08.MIT.EDU [18.216.0.136]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jB61RYMv026331 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 20:27:39 -0500 (EST) Message-ID: <4394E8E5.8090409@mit.edu> Date: Mon, 05 Dec 2005 20:27:01 -0500 From: Chris Wong 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: [Sayan] Week 14 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: 1150 Content-Length: 100 X-Keywords: NotJunk I would like clarification on when to use standard deviation and when to use variance.(pgs 14-16) From icharny@MIT.EDU Mon Dec 5 21:26:20 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 jB62QK6N000561 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 21:26:20 -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 jB62QJN1023025 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 21:26:19 -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 jB62QI9L003938 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 21:26:19 -0500 (EST) Received: from [127.0.0.1] (EASTCAMPUS-NINE-EIGHTY-THREE.MIT.EDU [18.238.6.216]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jB62QCMw029663 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 21:26:16 -0500 (EST) Message-ID: <4394F6C5.7040907@mit.edu> Date: Mon, 05 Dec 2005 21:26:13 -0500 From: Isaac Charny 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: [Sayan] Week 14 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: 1151 Content-Length: 130 X-Keywords: NonJunk NotJunk I don't really understand variance, what it is, and how to quickly calculate it. Please cover this in the next lecture. ~Isaac From vixen@MIT.EDU Mon Dec 5 23:40:24 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 jB64eO6N016167 for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 23:40:24 -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 jB64eMNc005741 for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 23:40:22 -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 jB64eFC3004626 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Mon, 5 Dec 2005 23:40:16 -0500 (EST) Mime-Version: 1.0 X-Sender: vixen@hesiod Message-Id: Date: Mon, 5 Dec 2005 23:38:10 -0500 To: 6042-probs@theory.lcs.mit.edu From: Amanda Seybold Subject: LN14 Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Spam-Score: 2.706 X-Spam-Level: ** (2.706) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1152 Content-Length: 60 X-Keywords: NotJunk I was confused as to what "x" was in many of the equations. From hkhall@MIT.EDU Mon Dec 5 23:48:48 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 jB64mm6N016611 for <6042-probs@theory.csail.mit.edu>; Mon, 5 Dec 2005 23:48:48 -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 jB64mkNc012499; Mon, 5 Dec 2005 23:48:46 -0500 (EST) Received: from [18.96.6.44] (SIMMONS-TWO-NINETY-NINE.MIT.EDU [18.96.6.44]) (authenticated bits=0) (User authenticated as hkhall@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB64mcI6006440 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT); Mon, 5 Dec 2005 23:48:39 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v623) Content-Type: text/plain; charset=US-ASCII; format=flowed Message-Id: <24b9be0d51a5c9b1398b83895ce0c687@mit.edu> Content-Transfer-Encoding: 7bit From: Harrison King Hall Subject: [David] Week 14 Comments Date: Mon, 5 Dec 2005 23:48:37 -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: 1153 Content-Length: 751 X-Keywords: NotJunk David- Even after our talk today I still had trouble with variance and using it to apply Chebyshev's theorem. For that matter is is taking me a long time to figure out Markov's as well. I think that I will get it by the time we go over it in class. I think that my problem lies in the fact that I don't really get E[R-c] where R is a random variable and c is some constant. I think this can be explained by linearity of expectation and E[c]=c, but I am not sure. Well, that is all I have to say, but I need to tell you that there is a high probability that I will not be in class on Friday since I have an away swim meet. I will get back to you on the exact time that I will be leaving and whether it means I will miss class. -Harrison From medrano@MIT.EDU Tue Dec 6 03:16:13 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 jB68GD6N021623 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 03:16:13 -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 jB68GBf0019816 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 03:16:11 -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 jB68Fv71001143 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 03:16:00 -0500 (EST) Subject: [sayan] final weekly question. finally From: Jesus Medrano To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Tue, 06 Dec 2005 03:15:58 +0000 Message-Id: <1133838958.10992.4.camel@localhost> Mime-Version: 1.0 X-Mailer: Evolution 2.2.3 Content-Transfer-Encoding: 7bit X-Spam-Score: 3.184 X-Spam-Level: *** (3.184) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1154 Content-Length: 462 X-Status: A X-Keywords: NotJunk Hi Sayan, My question is: is the Markov Theorem actually used in practice? It does not seem to be a great bound. The last problem in the tutor problem to be true. Also I kept submitting the same answer it kept telling me it was wrong and eventually it said it was right. I had to kept with a friend to make sure I was doing it right and he submitted the same answer I did and it said it was wrong. So my question again is Why Markov? Why?! Jesus Medrano From lye@MIT.EDU Tue Dec 6 09:54:05 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 jB6Es56N018000 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 09:54:05 -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 jB6Es3r1017665 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 09:54:04 -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 jB6ErvdH023351 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 09:53:57 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-6.mit.edu (8.12.4) id jB6Erv4u015269; Tue, 6 Dec 2005 09:53:57 -0500 Received: from RANDOM-ONE-FORTY-FOUR.MIT.EDU (RANDOM-ONE-FORTY-FOUR.MIT.EDU [18.243.5.144]) (User authenticated as lye@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 6 Dec 2005 09:53:57 -0500 Message-ID: <20051206095357.oo1wznsrikvwcgok@webmail.mit.edu> Date: Tue, 6 Dec 2005 09:53:57 -0500 From: Linda Ye To: 6042-probs@theory.lcs.MIT.EDU Subject: [Sayan] Week 14 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: 1155 Content-Length: 117 X-Status: A X-Keywords: NotJunk Is there a general way of calculating E[X^2] (like a nice compact formula)? What about for continuous distributions? From cbossard@MIT.EDU Tue Dec 6 12:00:50 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 jB6H0o6N016856 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 12:00:50 -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 jB6H0m7G023929 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 12:00:48 -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 jB6H0fvK023857 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 12:00:42 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jB6H0fkb022078; Tue, 6 Dec 2005 12:00:41 -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 ; Tue, 6 Dec 2005 12:00:41 -0500 Message-ID: <20051206120041.763rwy9139c4gkwg@webmail.mit.edu> Date: Tue, 6 Dec 2005 12:00:41 -0500 From: cbossard@MIT.EDU To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] Week 14 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: 1156 Content-Length: 256 X-Status: A X-Keywords: NonJunk NotJunk I am a little confused about Chebyshev's inequality in terms of standard deviation. Also on the TP I dont understand why to get 6,000 more than the other candidate you don't just need half + 6,000 but it keeps telling me that 3,006,000 is wrong. Cynthia From rnjacobs@MIT.EDU Tue Dec 6 13:54:29 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 jB6IsT6N019081 for <6042-probs@theory.csail.MIT.EDU>; Tue, 6 Dec 2005 13:54:29 -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 jB6Is37G009720 for <6042-probs@theory.csail.MIT.EDU>; Tue, 6 Dec 2005 13:54:03 -0500 (EST) Received: from m2-225-10.mit.edu (M2-225-10.MIT.EDU [18.21.0.92]) (authenticated bits=56) (User authenticated as rnjacobs@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB6Iruk6014081 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.MIT.EDU>; Tue, 6 Dec 2005 13:53:57 -0500 (EST) Received: (from rnjacobs@localhost) by m2-225-10.mit.edu (8.12.9) id jB6Is04d025614; Tue, 6 Dec 2005 13:54:00 -0500 Message-Id: <200512061854.jB6Is04d025614@m2-225-10.mit.edu> To: 6042-probs@theory.csail.MIT.EDU Subject: [Jelani] Reading response Date: Tue, 06 Dec 2005 13:54:00 -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: 1157 Content-Length: 53 X-Keywords: NonJunk NotJunk Nope, nothing new in the reading. - Robert Jacobs From meyer@imap.theory.csail.mit.edu Tue Dec 06 15:28:38 2005 Message-ID: <4395F47E.3050109@csail.mit.edu> Date: Tue, 06 Dec 2005 15:28:46 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Jesus Medrano Subject: Re: [sayan] final weekly question. finally References: <1133838958.10992.4.camel@localhost> In-Reply-To: <1133838958.10992.4.camel@localhost> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 882 X-UID: 1158 X-Keywords: Tutor behaved properly for me and answers are correct. Which part of the last problem did you find the tutor to be responding inconsistently on? Anyway, Markov rarely gives a good bound all by itself, but can be powerful when combined with other tricks. For example, by applying Markov to (R-m)^2, where m = E[R], we derive the Chebyshev bound about R. regards, A. Jesus Medrano wrote: > Hi Sayan, > > My question is: is the Markov Theorem actually used in practice? It does > not seem to be a great bound. The last problem in the tutor problem to > be true. Also I kept submitting the same answer it kept telling me it > was wrong and eventually it said it was right. I had to kept with a > friend to make sure I was doing it right and he submitted the same > answer I did and it said it was wrong. So my question again is > Why Markov? Why?! > > Jesus Medrano > From meyer@imap.theory.csail.mit.edu Tue Dec 06 15:31:01 2005 Message-ID: <4395F50D.9030304@csail.mit.edu> Date: Tue, 06 Dec 2005 15:31:09 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: cbossard@MIT.EDU Subject: Re: [David] Week 14 reading comments References: <20051206120041.763rwy9139c4gkwg@webmail.mit.edu> In-Reply-To: <20051206120041.763rwy9139c4gkwg@webmail.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 466 X-UID: 1159 X-Keywords: The total # of votes is fixed, so if one candidate got 6000 over the mean, the other would have to get 6000 BELOW the mean, so the diff would be 12,000. regards, A. cbossard@MIT.EDU wrote: > I am a little confused about Chebyshev's inequality in terms of > standard deviation. > > Also on the TP I dont understand why to get 6,000 more than the other > candidate you don't just need half + 6,000 but it keeps telling me > that 3,006,000 is wrong. > > Cynthia From meyer@imap.theory.csail.mit.edu Tue Dec 06 15:37:36 2005 Message-ID: <4395F698.8010402@csail.mit.edu> Date: Tue, 06 Dec 2005 15:37:44 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Linda Ye Subject: Re: [Sayan] Week 14 Comments References: <20051206095357.oo1wznsrikvwcgok@webmail.mit.edu> In-Reply-To: <20051206095357.oo1wznsrikvwcgok@webmail.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Status: RO Content-Length: 560 X-UID: 1160 X-Keywords: We don't do continuous distributions in discrete Math :-), though replacing our sums by integrals (of suitable kind) often allows discrete results to carry over to the continuous case. And no, there's no closed form formula for E[X^2] in terms of say, E[X]. But for the kind of simple X's we consider, it's usually possible to calculate E[X^2] from first principles using the def and linearity of E[]. regards, A Linda Ye wrote: > Is there a general way of calculating E[X^2] (like a nice compact formula)? What > about for continuous distributions? From meyer@imap.theory.csail.mit.edu Tue Dec 06 16:09:46 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 jB6L9j6N000382 for ; Tue, 6 Dec 2005 16:09:45 -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 1Ejk4H-0000Iz-FM for meyer@csail.mit.edu; Tue, 06 Dec 2005 16:09:45 -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 jB6L9i9a004763 for ; Tue, 6 Dec 2005 16:09:44 -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 jB6L9YGU016808 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for ; Tue, 6 Dec 2005 16:09:37 -0500 (EST) Subject: Re: [sayan] final weekly question. finally From: Jesus Medrano To: "Prof. Albert R. Meyer" In-Reply-To: <4395F47E.3050109@csail.mit.edu> References: <1133838958.10992.4.camel@localhost> <4395F47E.3050109@csail.mit.edu> Content-Type: text/plain Date: Tue, 06 Dec 2005 16:09:35 +0000 Message-Id: <1133885376.27912.1.camel@localhost> Mime-Version: 1.0 X-Mailer: Evolution 2.2.3 X-Spam-Score: 1.695 X-Scanned-By: MIMEDefang 2.42 Content-Transfer-Encoding: 7bit X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on theory.csail.mit.edu X-Spam-Level: X-Spam-Status: No, hits=-4.5 required=3.7 tests=AWL,BAYES_00, DATE_IN_PAST_03_06 autolearn=no version=2.63 Status: RO Content-Length: 1180 X-UID: 1161 X-Keywords: NotJunk Part 3 of the last problem. I put 1000/1001 and 1000 / 1001 and many combinations with different spacing and I received the x mark on all of them. Then out of nowhere it worked. Jesus On Tue, 2005-12-06 at 15:28 -0500, Prof. Albert R. Meyer wrote: > Tutor behaved properly for me and answers are correct. Which part of > the last problem did you find the tutor to be responding inconsistently on? > > Anyway, Markov rarely gives a good bound all by itself, but can be > powerful when combined with other tricks. For example, by applying > Markov to (R-m)^2, where m = E[R], we derive the Chebyshev bound about R. > > regards, A. > > > Jesus Medrano wrote: > > Hi Sayan, > > > > My question is: is the Markov Theorem actually used in practice? It does > > not seem to be a great bound. The last problem in the tutor problem to > > be true. Also I kept submitting the same answer it kept telling me it > > was wrong and eventually it said it was right. I had to kept with a > > friend to make sure I was doing it right and he submitted the same > > answer I did and it said it was wrong. So my question again is > > Why Markov? Why?! > > > > Jesus Medrano > > From meyer@imap.theory.csail.mit.edu Tue Dec 06 16:59:11 2005 Message-ID: <439609AF.7010602@csail.mit.edu> Date: Tue, 06 Dec 2005 16:59:11 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Jesus Medrano CC: 6042-online-tutor@theory.csail.mit.edu Subject: Re: [sayan] final weekly question. finally References: <1133838958.10992.4.camel@localhost> <4395F47E.3050109@csail.mit.edu> <1133885376.27912.1.camel@localhost> In-Reply-To: <1133885376.27912.1.camel@localhost> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 1321 Status: RO X-UID: 1162 X-Keywords: Ok, I'm cc'ing the tutor-master to watch for similar probs. thx for the info. regards, A. Jesus Medrano wrote: >Part 3 of the last problem. I put 1000/1001 and 1000 / 1001 and many >combinations with different spacing and I received the x mark on all of >them. Then out of nowhere it worked. > >Jesus > >On Tue, 2005-12-06 at 15:28 -0500, Prof. Albert R. Meyer wrote: > > >>Tutor behaved properly for me and answers are correct. Which part of >>the last problem did you find the tutor to be responding inconsistently on? >> >>Anyway, Markov rarely gives a good bound all by itself, but can be >>powerful when combined with other tricks. For example, by applying >>Markov to (R-m)^2, where m = E[R], we derive the Chebyshev bound about R. >> >>regards, A. >> >> >>Jesus Medrano wrote: >> >> >>>Hi Sayan, >>> >>>My question is: is the Markov Theorem actually used in practice? It does >>>not seem to be a great bound. The last problem in the tutor problem to >>>be true. Also I kept submitting the same answer it kept telling me it >>>was wrong and eventually it said it was right. I had to kept with a >>>friend to make sure I was doing it right and he submitted the same >>>answer I did and it said it was wrong. So my question again is >>>Why Markov? Why?! >>> >>>Jesus Medrano >>> >>> >>> From hectorb@MIT.EDU Tue Dec 6 18:25:01 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 jB6NP16N008100 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 18:25:01 -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 jB6NP0xb029651 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 18:25:00 -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 jB6NOvVa006661 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 18:24:58 -0500 (EST) Message-ID: <43961DC4.3060601@mit.edu> Date: Tue, 06 Dec 2005 18:24:52 -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.lcs.mit.edu Subject: [Hanson] Week 14 Reading Comment 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: 1163 Content-Length: 374 X-Keywords: NonJunk NotJunk "High variance is often associated with high risk. For example, in ten rounds of Game A, we expect to make $10, but could conceivably lose $10 instead. On the other hand, in ten rounds of game B, we also expect to make $10, but could actually lose more than $20,000!" -p.14 I found this example interesting. I enjoy reading the examples that involve gambling. -Hector From dowgun@MIT.EDU Tue Dec 6 18:42:15 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 jB6NgF6N013462 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 18:42:15 -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 jB6NgExb015618 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 18:42:14 -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 jB6NgCoB010923 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 6 Dec 2005 18:42:12 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-5.mit.edu (8.12.4) id jB6NgCwV016235; Tue, 6 Dec 2005 18:42:12 -0500 Received: from PLP-FORTY-SIX.MIT.EDU (PLP-FORTY-SIX.MIT.EDU [18.218.1.46]) (User authenticated as dowgun@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 6 Dec 2005 18:42:12 -0500 Message-ID: <20051206184212.295phtwjiggowoos@webmail.mit.edu> Date: Tue, 6 Dec 2005 18:42:12 -0500 From: Neil M Dowgun To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] ln 14 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: 1164 Content-Length: 430 X-Status: A X-Keywords: NotJunk I feel like I must be misunderstanding variance, because it seems incredibly difficult to calculate for problems that don't have only two outcomes (say, the third problem on the tutor problems). I mean, if you flip a fair coin 100 times, then to get E(A - E(A))^2 you have to calculate the probability of each and every value of A coming up, right? And then add them all up? There has to be an easier way to do this. Thanks, Neil From meyer@imap.theory.csail.mit.edu Tue Dec 06 20:57:01 2005 Message-ID: <4396416E.6030703@csail.mit.edu> Date: Tue, 06 Dec 2005 20:57:02 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Neil M Dowgun Subject: Re: [Hanson] ln 14 References: <20051206184212.295phtwjiggowoos@webmail.mit.edu> In-Reply-To: <20051206184212.295phtwjiggowoos@webmail.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 603 Status: RO X-UID: 1165 X-Keywords: the variance is 100 times the variance of one flip (which is1/2(1-1/2) = 1/4) so the answer is 100(1/4)=25; see Notes 14, section 8.3. Neil M Dowgun wrote: >I feel like I must be misunderstanding variance, because it seems incredibly >difficult to calculate for problems that don't have only two outcomes (say, the >third problem on the tutor problems). I mean, if you flip a fair coin 100 times, >then to get E(A - E(A))^2 you have to calculate the probability of each and >every value of A coming up, right? And then add them all up? There has to be an >easier way to do this. >Thanks, Neil > > From petek@MIT.EDU Tue Dec 6 21:50:05 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 jB72o56N018847 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 21:50:05 -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 jB72o4vM015882 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 21:50:04 -0500 (EST) Received: from [18.194.1.37] (SN-THIRTY-SEVEN.MIT.EDU [18.194.1.37]) (authenticated bits=0) (User authenticated as petek@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB72nvrG018151 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 21:49:58 -0500 (EST) Message-ID: <43964DE4.2020005@mit.edu> Date: Tue, 06 Dec 2005 21:50:12 -0500 From: Pete Kruskall 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: [Jelani] Markov+ Chebsnsvlskjdfslky Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Spam-Score: 4.562 X-Spam-Level: **** (4.562) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1166 Content-Length: 1030 X-Status: A X-Keywords: NonJunk NotJunk Despite the fact that my eyes / brain refuse to take the effort to actually pronounce the second man's name, I got through this week's notes in an ok manner.  I'm having trouble getting the last TP prob right.  Given standard dev = 2000, and you want the pr that gore gets 6,000 more votes, shouldn't the prob be bounded by (standard dev)^2 / (6,000)^2  =  1/9? 

Also, this week's notes is a good example of stuff that rather than make a good home in my head will probably make a much better one on the crib sheet we bring into the exam.

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

:::::::::::::::::::::::::::::
508.843.5861 ::::Cell Phone::
617.536.9925 :::Sigma Nu:::::
From mracich@MIT.EDU Tue Dec 6 23:35:39 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 jB74Zd6N015096 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:35:39 -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 jB74ZcSt011822 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:35:38 -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 jB74ZcIj005445 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:35:38 -0500 (EST) Received: from MACGREGOR-TWO-FIFTY-NINE.MIT.EDU (MACGREGOR-TWO-FIFTY-NINE.MIT.EDU [18.239.6.4]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jB74ZZok007795 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:35:35 -0500 (EST) Subject: [Sayan] Comments for Course Notes, Week 14 (Missed Expectations?) From: Moira Racich To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Tue, 06 Dec 2005 23:35:34 -0500 Message-Id: <1133930134.8131.5.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: 1167 Content-Length: 274 X-Keywords: NotJunk I found all of section 7, "Chebyshev's Theorem", (starting on page 12) incredibly confusing. I also had a very hard time with the tutor problem questions that related to this material. I would appreciate it if this section was reviewed in depth. Thanks, Moira Racich From rian@MIT.EDU Tue Dec 6 23:40:50 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 jB74eo6N015450 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:40:50 -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 jB74enYe009708 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:40:49 -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 jB74ek0b010708 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:40:47 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Rian Hunter Subject: [jelani] - week 14 comments Date: Tue, 6 Dec 2005 23:40:45 -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: 1168 Content-Length: 585 X-Keywords: NotJunk This week's reading is very long, lots of concepts to learn and/or equations to memorize. I'd like to request that when the class is tested on this material, it isn't very very rigorous since to adequately absorb this material and apply it, it will take longer than a week or at least I think so. Variance and Chebyshev's Theorem seem clear and sensible to me but in class I would like to see more applications of these tools to gain a better grasp of the topics. Also way more examples of ways to calculate variance in different circumstances or problems. Rian Hunter From ridell@MIT.EDU Tue Dec 6 23:42:31 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 jB74gV6N015589 for <6042-probs@theory.csail.MIT.EDU>; Tue, 6 Dec 2005 23:42:31 -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 jB74gUYe010921 for <6042-probs@theory.csail.MIT.EDU>; Tue, 6 Dec 2005 23:42:30 -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 jB74gSMq011018 for <6042-probs@theory.csail.MIT.EDU>; Tue, 6 Dec 2005 23:42:28 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jB74gSii030633; Tue, 6 Dec 2005 23:42:28 -0500 Received: from NEXT-NINE.MIT.EDU (NEXT-NINE.MIT.EDU [18.242.5.9]) (User authenticated as ridell@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 6 Dec 2005 23:42:28 -0500 Message-ID: <20051206234228.nqov9g9yta1w0kg4@webmail.mit.edu> Date: Tue, 6 Dec 2005 23:42:28 -0500 From: Rebecca Idell To: 6042-probs@theory.csail.MIT.EDU Subject: tp 14 reading comments [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: 1169 Content-Length: 271 X-Keywords: NonJunk NotJunk Can you give more examples of problems with Markov's thm from p10 of the reading? -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 tonyng@MIT.EDU Tue Dec 6 23:57:30 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 jB74vU6N020683 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:57:30 -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 jB74vTYe021563 for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:57:29 -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 jB74vMwr013673 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 6 Dec 2005 23:57:23 -0500 (EST) Message-Id: <5.2.1.1.2.20051206234656.0214fea0@po9.mit.edu> X-Sender: tonyng@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Tue, 06 Dec 2005 23:57:01 -0500 To: 6042-probs@theory.lcs.mit.edu From: Tony Ng Subject: [Jelani] Reading Comments Week 14 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: 1170 Content-Length: 214 X-Keywords: NotJunk I have a question on theorem 4.2 on pg8. Given two independent random variables A and B, E[A*B] = E[A]*E[B]. However, is it true backwards? Does E[A]*E[B] = E[A*B] imply that A and B are independent? - Tony Ng From ereid@MIT.EDU Wed Dec 7 00:07:53 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 jB757r6N025934 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:07:53 -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 jB757qYe028747 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:07:52 -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 jB757kDO015962 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:07:50 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v734) Content-Transfer-Encoding: 7bit Message-Id: Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Elizabeth Reid Subject: [Hanson] Reading Comment Date: Wed, 7 Dec 2005 00:07:43 -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: 1171 Content-Length: 210 X-Status: A X-Keywords: NonJunk NotJunk The definition used for Variance and Standard Deviation seem like overly complicated ones. Maybe it's just the shorthand used, but it's a lot less intuitive this way than other ways that I have learned it. From jehan@MIT.EDU Wed Dec 7 00:40:01 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 jB75e16N005758 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 00:40:01 -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 jB75e0Ye021180 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 00:40:00 -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 jB75diYL020682 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 00:39:44 -0500 (EST) Message-Id: <5.2.1.1.2.20051207003453.00bc3678@po14.mit.edu> X-Sender: jehan@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 07 Dec 2005 00:37:48 -0500 To: 6042-probs@theory.csail.mit.edu From: Jehan deFonseka Subject: [Sayan] Week 14 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: 1172 Content-Length: 72 X-Keywords: NonJunk NotJunk No questions. I thought Markov's approximation was pretty cool. jehan From avalys@MIT.EDU Wed Dec 7 00:42:53 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 jB75gr6N006269 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:42:53 -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 jB75gqYe023163 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:42:52 -0500 (EST) Received: from [18.96.6.214] (SIMMONS-FOUR-SIXTY-NINE.MIT.EDU [18.96.6.214]) (authenticated bits=0) (User authenticated as avalys@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB75gn63021101 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:42:50 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: <2C7AD70A-F06B-4655-8E53-8759C266EA5D@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: Wed, 7 Dec 2005 00:42:51 -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: 1173 Content-Length: 174 X-Keywords: NonJunk NotJunk I am a little unclear about how to use the alternative expression of variance described in section 8.2 (page 8). How is one supposed to find the value of E[R^2]? Alex From yangc@MIT.EDU Wed Dec 7 00:43:45 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 jB75hi6N006325 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 00:43:44 -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 jB75hhYe023814 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 00:43:43 -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 jB75hcLr021194 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 00:43:41 -0500 (EST) Message-Id: <200512070543.jB75hcLr021194@outgoing.mit.edu> From: "Chris Yang" To: <6042-probs@theory.csail.mit.edu> Subject: [David] Week 14 Comments Date: Wed, 7 Dec 2005 00:43:37 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0043_01C5FAC7.44623590" X-Mailer: Microsoft Office Outlook, Build 11.0.5510 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcX68StIqMReESUKT/OUXquD7Sjetg== X-Spam-Score: 2.038 X-Spam-Level: ** (2.038) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1174 Content-Length: 2191 X-Keywords: NonJunk NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_0043_01C5FAC7.44623590 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Oh my God, I don't understand Variance or the two theorems about the upper/lower bounds at all. Please tell me we are going over this in class. Thanks, Chris Yang ------=_NextPart_000_0043_01C5FAC7.44623590 Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: quoted-printable

Oh my God, I don’t understand Variance or the = two theorems about the upper/lower bounds at all.  Please tell me we = are going over this in class.

 

Thanks,

Chris Yang

------=_NextPart_000_0043_01C5FAC7.44623590-- From hzhou@MIT.EDU Wed Dec 7 00:46:07 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 jB75k76N006614 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:46:07 -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 jB75k6Ye025398 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:46:06 -0500 (EST) Received: from hzhou.mit.edu (BURTON-NINETY-FIVE.MIT.EDU [18.247.5.95]) (authenticated bits=0) (User authenticated as hzhou@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB75k4vd021573 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 00:46:04 -0500 (EST) Message-Id: <5.2.1.1.2.20051207003858.02aa40a0@po9.mit.edu> X-Sender: hzhou@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 07 Dec 2005 00:46:21 -0500 To: 6042-probs@theory.lcs.mit.edu From: Steven Zhou Subject: [David] tp-14 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: 1175 Content-Length: 263 X-Keywords: NonJunk NotJunk Hi, Topic is clear. I have a question for problem set number 5. With the answer i got for (a), if i were to solve for K that minimized that expression, I get a quadratic equation. Is it that complicated, or did I do part (a) wrong. Thanks. - Steven Zhou From mukkala@MIT.EDU Wed Dec 7 01:00:06 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 jB76066N012155 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 01:00:06 -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 jB7605Ye004427 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 01:00:05 -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 jB75xvFU023437 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 00:59:58 -0500 (EST) Message-Id: <6.2.1.2.2.20051207001238.01f2fe20@po12.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.1.2 Date: Wed, 07 Dec 2005 00:59:55 -0500 To: 6042-probs@theory.csail.mit.edu From: Praveen Pamidimukkala Subject: [Sayan] Week 14 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) 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 jB76066N012155 Status: RO X-UID: 1176 Content-Length: 535 X-Keywords: NotJunk Hi, My question pertains to the TP as opposed to the reading. In TP.14.3, it reads: "Suppose you flip a fair coin 100 times. The coin flips are all mutually independent. 3. What is the variance of the number of heads? Let Xi be the random variable whose value is 1 if the ith coin flip is heads. Then Var[Xi] = 1/2 - (1/2)2 = 1/4. So Var[X1 + ... + X100] = 100·(1/4) = 25. (Note we can use additivity of variance here since our flips are independent.) ] " I don't understand the calculation for Var[Xi]. Thanks, Praveen From dnreshef@MIT.EDU Wed Dec 7 01:05:43 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 jB765h6N012498 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:05:43 -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 jB765fYe008369 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:05:42 -0500 (EST) Received: from w92-130-webmail-4.mit.edu (W92-130-WEBMAIL-4.MIT.EDU [18.7.22.135]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB765Y79024272 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:05:34 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-4.mit.edu (8.12.4) id jB765YGE025250; Wed, 7 Dec 2005 01:05:34 -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, 7 Dec 2005 01:05:34 -0500 Message-ID: <20051207010534.pihvlgyaiyckwgks@webmail.mit.edu> Date: Wed, 7 Dec 2005 01:05:34 -0500 From: David N Reshef To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] Reading Comments 14 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: 1177 Content-Length: 287 X-Keywords: This week's reading was particularly technical and cumbersome. I had the most trouble understanding condeitional expectation and variance. Could we please go over variance real quickly in class, I know it's not a really hard concept, I just don't really understand it quite yet. -Dave From lmccart@MIT.EDU Wed Dec 7 01:11:46 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 jB76Bk6N013625 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:11:46 -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 jB76BjYe012308 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:11:45 -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 jB76Bh6K024949 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:11:43 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-6.mit.edu (8.12.4) id jB76Bh5V009935; Wed, 7 Dec 2005 01:11:43 -0500 Received: from 18.153.1.172 ([18.153.1.172]) (User authenticated as lmccart@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 7 Dec 2005 01:11:43 -0500 Message-ID: <20051207011143.kx8gkdpnkrcwsccw@webmail.mit.edu> Date: Wed, 7 Dec 2005 01:11:43 -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: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1178 Content-Length: 95 X-Keywords: NotJunk The topic of standard deviation was a little bit confusing but everything else was very clear. From ctsims@MIT.EDU Wed Dec 7 01:23:21 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 jB76NL6N019398 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 01:23:21 -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 jB76NJYe019796 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 01:23:20 -0500 (EST) Received: from HowardRoark.mit.edu (EASTCAMPUS-EIGHT-TWELVE.MIT.EDU [18.238.6.45]) (authenticated bits=0) (User authenticated as ctsims@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB76NGgC026240 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 01:23:17 -0500 (EST) Message-Id: <5.2.1.1.2.20051207011740.0303ae80@po12.mit.edu> X-Sender: ctsims@po12.mit.edu X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 07 Dec 2005 01:21:06 -0500 To: 6042-probs@theory.lcs.mit.edu From: Clayton Sims Subject: [6.042] Reading Comment Lecture Notes 14 - 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: 1179 Content-Length: 295 X-Keywords: NonJunk NotJunk I found that the definition of Variance using a the expectation of (random variable minus it's expected value) squared) defined on page 13, and used in the next 3 or 4 pages, to be hard to apply to some real world cases. It would be nice to have it more fully explained in class. -Clayton From jjmonzon@MIT.EDU Wed Dec 7 01:24:33 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 jB76OX6N019643 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 01:24:33 -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 jB76OWYe020538 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 01:24:32 -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 jB76OQpx026362 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 01:24:29 -0500 (EST) Message-Id: <6.2.3.4.2.20051207012427.01d8a630@po9.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Wed, 07 Dec 2005 01:24:29 -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: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1180 Content-Length: 336 X-Status: A X-Keywords: NonJunk NotJunk I liked the section about inequalities (Markov and Chebyshev) - they are very great at giving bounds. I am just wondering if Central Limit Theorem is going to be introduced in this class. Josh Joshua Jen C. Monzon Massachusetts Institute of Technology Electrical Engineering with Computer Science jjmonzon@mit.edu 617-803-7497 From pgroudas@MIT.EDU Wed Dec 7 01:37:45 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 jB76bj6N028640 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:37:45 -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 jB76biYe028619 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:37:44 -0500 (EST) Received: from w92-130-webmail-4.mit.edu (W92-130-WEBMAIL-4.MIT.EDU [18.7.22.135]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB76bgMG027648 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 01:37:42 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-4.mit.edu (8.12.4) id jB76bg2d027834; Wed, 7 Dec 2005 01:37:42 -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 ; Wed, 7 Dec 2005 01:37:42 -0500 Message-ID: <20051207013742.lbmgldl6544kw4w0@webmail.mit.edu> Date: Wed, 7 Dec 2005 01:37:42 -0500 From: Paul Groudas To: 6042-probs@theory.lcs.MIT.EDU Subject: [HANSON] Week 14 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: 1182 Content-Length: 250 X-Keywords: NotJunk I thought the reading was okay, but shouldn't there have been a section on binomial standard deviation? Was this just covered already or something? I needed to look it up on the web so i could get the variance for one of the tutor problems. -Paul From shreyes19@gmail.com Wed Dec 7 01:43:15 2005 Return-Path: Received: from nproxy.gmail.com (nproxy.gmail.com [64.233.182.202]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jB76hF6N030315 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 01:43:15 -0500 Received: by nproxy.gmail.com with SMTP id d4so87495nfe for <6042-probs@theory.lcs.mit.edu>; Tue, 06 Dec 2005 22:43:14 -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=rINwFbOa1dAqS/8rKF3DDanQs+RotpMUQInBgRLEsw+QRpf+yZ5vEcp+tac9JPP8ENgxI6F2byJZ/huzSeYyfA73GcXYNQH+DzzIP0EtEvgU8dkdCYhxmnQG3PXlxcrqJWRaey3XC0xZl/2TTdoCEpjCU9jfNDeC4CGqe8BdaMU= Received: by 10.48.164.14 with SMTP id m14mr18498nfe; Tue, 06 Dec 2005 22:43:14 -0800 (PST) Received: by 10.48.127.11 with HTTP; Tue, 6 Dec 2005 22:43:14 -0800 (PST) Message-ID: <3c33fe380512062243t452e6f37ic72aa43637dbff44@mail.gmail.com> Date: Wed, 7 Dec 2005 01:43:14 -0500 From: Shreyes Seshasai Sender: shreyes19@gmail.com To: 6042-probs@theory.lcs.mit.edu Subject: [Sayan] Week 14 Reading Comments MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_13968_10334097.1133937794310" Status: RO X-UID: 1183 Content-Length: 2042 X-Keywords: NonJunk NotJunk ------=_Part_13968_10334097.1133937794310 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Hi, Comments on the reading for this week: My comments deal with the two inequalities presented, Markov's (on page 10) and Chebyshev's (on page 12). The calculations required for both of these make sense to me and don't seem too difficult, but one thing I'd like to se= e discussed in class is the types of problems that each of these can help resolve, and suggestions on how to decide which inequality to choose when given a problem. I know Markov's inequality deals with the values greater than a specified number, but could Chebyshev's be used as well with careful selection of x in the inequality. (Hopefully the answer to this is better than the one given in 6.041 this morning, that Chebyshev's has an x^2 in th= e denominator, so when given a bound of that form, use that inequality). Thanks, Shreyes ------=_Part_13968_10334097.1133937794310 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Hi,

Comments on the reading for this week:

My comments deal with the two inequalities presented, Markov's (on page 10) and Chebyshev's (on page 12).  The calculations required for both of these make sense to me and don't seem too difficult, but one thing I'd like to see discussed in class is the types of problems that each of these can help resolve, and suggestions on how to decide which inequality to choose when given a problem.  I know Markov's inequality deals with the values greater than a specified number, but could Chebyshev's be used as well with careful selection of x in the inequality.  (Hopefully the answer to this is better than the one given in 6.041 this morning, that Chebyshev's has an x^2 in the denominator, so when given a bound of that form, use that inequality).


Thanks,
Shreyes
------=_Part_13968_10334097.1133937794310-- From jeffhoff@MIT.EDU Wed Dec 7 02:08:26 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 jB778Q6N007867 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 02:08:26 -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 jB778PJh015920 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 02:08:25 -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 jB7766qN000145 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 02:06:47 -0500 (EST) Message-Id: <6.2.3.4.2.20051207020413.01e2a200@hesiod> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Wed, 07 Dec 2005 02:06:03 -0500 To: 6042-probs@theory.csail.mit.edu From: "Jeffrey D. Hoff" Subject: [Hanson] Week 14 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: 1184 Content-Length: 165 X-Keywords: NonJunk NotJunk Page 13 Section 7.0 Variance! I don't get it. I can't calculate it. The binomial example didn't really help much. Can we get a better example with real numbers? From mpapi@MIT.EDU Wed Dec 7 03:04:56 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 jB784u6N021765 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 03:04:56 -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 jB784tJh017910 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 03:04:55 -0500 (EST) Received: from mpapi.MIT.EDU (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 jB784qj7004187 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 03:04:53 -0500 (EST) Subject: [Jelani] week 14 comments From: Matt Papi To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Wed, 07 Dec 2005 03:08:59 -0500 Message-Id: <1133942939.5998.63.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.4.1 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: 1185 Content-Length: 226 X-Keywords: NonJunk NotJunk Section 7, on Chebyshev's theorem; I thought that the applications of Chebyshev's theorem (i.e. in the tutor problem) were pretty hard to grasp. I also don't really understand how it is derived from Markov's theorem. - Matt From mwangi@MIT.EDU Wed Dec 7 03:08:35 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 jB788Z6N022599 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 03:08:35 -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 jB788WJh019825; Wed, 7 Dec 2005 03:08:32 -0500 (EST) Received: from IBM-1E80C73FC15.mit.edu (NEW-SIXTY.MIT.EDU [18.241.5.60]) (authenticated bits=0) (User authenticated as mwangi@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB788Uge004373 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT); Wed, 7 Dec 2005 03:08:31 -0500 (EST) Message-Id: <6.2.1.2.2.20051207025356.03fd1eb0@po12.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.1.2 Date: Wed, 07 Dec 2005 03:08:27 -0500 To: 6042-probs@theory.lcs.mit.edu From: Timothy Mwangi Subject: [Sayan] Week 14 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: 1186 Content-Length: 372 X-Keywords: NotJunk Passage: 7 Chebyshev's Theorem Page: 12 I found this passage most surprising because of the very low probability of a random variable deviating more than a few standard deviations from the mean. I found it especially surprising because Chebyshev's Theorem can be applied to any random variable, regardless of what it's PDF is. Sincerely, Timothy M. Mwangi From meyer@imap.theory.csail.mit.edu Wed Dec 07 03:22:16 2005 Message-ID: <43969BB9.2040402@csail.mit.edu> Date: Wed, 07 Dec 2005 03:22:17 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Pete Kruskall Subject: Re: [Jelani] Markov+ Chebsnsvlskjdfslky References: <43964DE4.2020005@mit.edu> In-Reply-To: <43964DE4.2020005@mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 894 Status: RO X-UID: 1187 X-Keywords: if Gore got 6000 more votes, then he got 3000 ABOVE THE MEAN, and Bush got 3000 below, so the denominator should be (3000)^2. Regards, A. Pete Kruskall wrote: > Despite the fact that my eyes / brain refuse to take the effort to actually pronounce the second man's name, I got through this week's notes in an ok manner. I'm having trouble getting the last TP prob right. Given standard dev = 2000, and you want the pr that gore gets 6,000 more votes, shouldn't the prob be bounded by (standard dev)^2 / (6,000)^2 = 1/9? > > Also, this week's notes is a good example of stuff that rather than make a good home in my head will probably make a much better one on the crib sheet we bring into the exam. > > -P > >-- >Pete Kruskall >28 The Fenway >Boston, MA 02215 > >::::::::::::::::::::::::::::: >508.843.5861 ::::Cell Phone:: >617.536.9925 :::Sigma Nu::::: > From lana@MIT.EDU Wed Dec 7 03:41:14 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 jB78fE6N003973 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 03:41:14 -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 jB78fCJh007498 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 03:41:13 -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 jB78f6WB006051 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 03:41:06 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jB78f6mn006398; Wed, 7 Dec 2005 03:41:06 -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, 7 Dec 2005 03:41:06 -0500 Message-ID: <20051207034106.2sfpeg8bro08co80@webmail.mit.edu> Date: Wed, 7 Dec 2005 03:41:06 -0500 From: Svetlana Goldenberg To: 6042-probs@theory.lcs.MIT.EDU Subject: [Sayan] TP14 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: 1188 Content-Length: 215 X-Keywords: NotJunk The part that I found to be the most intriguing was the symmetry in the alternative definition of variance, particularly because the link between the original definition and this version is far from intuitive. Lana From lkini@MIT.EDU Wed Dec 7 03:52:19 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 jB78qJ6N007253 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 03:52:19 -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 jB78qIJh013853 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 03:52:18 -0500 (EST) Received: from [18.239.6.223] (MACGREGOR-FOUR-SEVENTY-EIGHT.MIT.EDU [18.239.6.223]) (authenticated bits=0) (User authenticated as lkini@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB78qA3s006610 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 03:52:12 -0500 (EST) Message-ID: <4396A2A8.4050800@mit.edu> Date: Wed, 07 Dec 2005 03:51:52 -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 14 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: 1189 Content-Length: 166 X-Keywords: NotJunk Hi Hanson, I found Chebyshev's Theorem most interesting cause it gives limits in the broadest of applications: from the birthday problem to the IQ example. Lohith From meyer@imap.theory.csail.mit.edu Wed Dec 07 04:12:18 2005 Message-ID: <4396A771.8040005@csail.mit.edu> Date: Wed, 07 Dec 2005 04:12:17 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Elizabeth Reid Subject: Re: [Hanson] Reading Comment References: In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 283 Status: RO X-UID: 1190 X-Keywords: What was your intuitive way? regards, A. Elizabeth Reid wrote: > The definition used for Variance and Standard Deviation seem like > overly complicated ones. Maybe it's just the shorthand used, but it's > a lot less intuitive this way than other ways that I have learned it. From meyer@imap.theory.csail.mit.edu Wed Dec 07 04:16:03 2005 Message-ID: <4396A854.8040201@csail.mit.edu> Date: Wed, 07 Dec 2005 04:16:04 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: "Joshua Jen C. Monzon" Subject: Re: [David] - Reading Comments References: <6.2.3.4.2.20051207012427.01d8a630@po9.mit.edu> In-Reply-To: <6.2.3.4.2.20051207012427.01d8a630@po9.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 557 Status: RO X-UID: 1191 X-Keywords: Central lim thm will be mentioned VERY briefly next week, along with an explanation of why it's not of central interest in engineering and computer science. regards, Joshua Jen C. Monzon wrote: > I liked the section about inequalities (Markov and Chebyshev) - they > are very great at giving bounds. I am just wondering if Central Limit > Theorem is going to be introduced in this class. > > Josh > > > > Joshua Jen C. Monzon > Massachusetts Institute of Technology > Electrical Engineering with Computer Science > jjmonzon@mit.edu 617-803-7497 > From fluff@MIT.EDU Wed Dec 7 04:39:23 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 jB79dN6N022792 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 04:39:23 -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 jB79dLJh008347 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 04:39:21 -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 jB79dEkT008578 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 04:39:15 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Crystal Chao Subject: [Jelani] week 14 reading Date: Wed, 7 Dec 2005 04:37:08 -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: 1192 Content-Length: 259 X-Keywords: NonJunk NotJunk I found all the examples about IQ really depressing. They just seem to highlight the fact that I don't understand something. I still don't intuitively get how you can just ignore dependence/independence for the linearity of expectation stuff. ~Crystal From benlu@MIT.EDU Wed Dec 7 08:09:11 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 jB7D9B6N025772 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 08:09:11 -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 jB7D99uB004719 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 08:09:10 -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 jB7D97EG022723 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 08:09:07 -0500 (EST) Message-ID: <4396DEF3.4050003@mit.edu> Date: Wed, 07 Dec 2005 08:09:07 -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 14 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: 1193 Content-Length: 354 X-Keywords: NotJunk Hey Jelani, It's cool to finally have a definition for variance and standard deviation! I've heard those terms thrown around so many times, and until now have had to rely on a purely intuitive understanding of what people meant. As for things that I don't understand, I mostly just need practice calculating those E(R^2) terms. Cheers, ~Ben Lu From kromer@MIT.EDU Wed Dec 7 10:01:41 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 jB7F1f6N011374 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 10:01:41 -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 jB7F1euB025552 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 10:01:40 -0500 (EST) Received: from m12-182-19.mit.edu (M12-182-19.MIT.EDU [18.19.0.50]) (authenticated bits=56) (User authenticated as kromer@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7F1Wt8027859 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 10:01:33 -0500 (EST) Received: (from kromer@localhost) by m12-182-19.mit.edu (8.12.9) id jB7F1WxY021379; Wed, 7 Dec 2005 10:01:32 -0500 (EST) 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, 07 Dec 2005 10:01:31 -0500 Message-Id: <1133967691.21236.9.camel@m12-182-19.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: 1194 Content-Length: 742 X-Keywords: NonJunk NotJunk "the expected value of a sum of random variables is the sum of the expected values of the variables" (p. 1) When we consider two random variables at the same time, I understand how we get the expectation of their sum, but how do we expect the values of the variables to be distributed? For example, say we're rolling two six-sided dice. We expect them to sum to 7, and each die individualy has an expected value of 3.5. Is the expected maximum of the dice 3.5, because that's the expectation of each die? It seems likely that one die would have a higher value than the other on most rolls, so it seems that the expected maximum must be larger than 3.5 and the expected minimum must be less--how would you go about computing this? Katherine From arup@MIT.EDU Wed Dec 7 10:09:07 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 jB7F976N016057 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:09:07 -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 jB7F95uB005291 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:09:05 -0500 (EST) Received: from [18.247.6.35] (BURTON-TWO-NINETY.MIT.EDU [18.247.6.35]) (authenticated bits=0) (User authenticated as arup@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7F8qQA001138 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:08:58 -0500 (EST) Message-ID: <4396FAE7.8000005@mit.edu> Date: Wed, 07 Dec 2005 10:08:23 -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 14 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: 1195 Content-Length: 239 X-Keywords: NonJunk NotJunk The coupon collector problem (section 2) is probably the most interesting section in this week's reading to me because I've seen most of the rest of it in my statistics class, I think. Most of it seemed pretty straightforward. |Arup| From ryoung@MIT.EDU Wed Dec 7 10:40:24 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 jB7FeO6N031865 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 10:40:24 -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 jB7FeNuB017076 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 10:40:23 -0500 (EST) Received: from ryan.mit.edu (PSK-SIXTEEN.MIT.EDU [18.217.1.16]) (authenticated bits=0) (User authenticated as ryan786@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7FeF9l015586 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 10:40:16 -0500 (EST) Message-Id: <6.2.3.4.2.20051207102936.02f0feb0@po10.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Wed, 07 Dec 2005 10:40:17 -0500 To: 6042-probs@theory.lcs.mit.edu From: ryan Subject: [sayan] 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: 1196 Content-Length: 177 X-Keywords: NonJunk NotJunk I had a really hard time with Chebyshev bounds, and couldn't even get them on the tutor problems for the longest time. I understand them now, but it took me a while. -Ryan From rshroff@MIT.EDU Wed Dec 7 10:43:24 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 jB7FhO6N002751 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 10:43:24 -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 jB7FhMuB021219 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 10:43:23 -0500 (EST) Received: from w92-130-webmail-4.mit.edu (W92-130-WEBMAIL-4.MIT.EDU [18.7.22.135]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7FhGdr016955 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 10:43:16 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-4.mit.edu (8.12.4) id jB7FhG6Z031822; Wed, 7 Dec 2005 10:43:16 -0500 Received: from QUICKSTATION-LOBBY-16-1.MIT.EDU (QUICKSTATION-LOBBY-16-1.MIT.EDU [18.55.1.64]) (User authenticated as rshroff@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 7 Dec 2005 10:43:16 -0500 Message-ID: <20051207104316.v98xqdxg8vyg40c4@webmail.mit.edu> Date: Wed, 7 Dec 2005 10:43:16 -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: -1.638 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1197 Content-Length: 119 X-Keywords: NonJunk NotJunk I found the properties of expectation and variance of trhe various distributions extremely interesting. -Rahul Shroff From zacharyozer@gmail.com Wed Dec 7 10:44:31 2005 Return-Path: Received: from zproxy.gmail.com (zproxy.gmail.com [64.233.162.204]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jB7FiV6N005151 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 10:44:31 -0500 Received: by zproxy.gmail.com with SMTP id o37so457467nzf for <6042-probs@theory.lcs.mit.edu>; Wed, 07 Dec 2005 07:44:30 -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=YY/xrE0qiVsOEQlGP4bi59t1VY0dHGm34+jkJ5SM1CIuIWABYUX7e0nhZEG0BJ5jVb50Vm+CGbZZG2x+ORZ8TrzgIAw8M1FK5yS6+eANi4lrTf2/aS2sAQzUIL/SvSiRWHa9c+TtJW3MOP79yazmYKb+SyfthxivNWYoadVEtvE= Received: by 10.64.220.17 with SMTP id s17mr1841538qbg; Wed, 07 Dec 2005 07:44:30 -0800 (PST) Received: by 10.64.27.3 with HTTP; Wed, 7 Dec 2005 07:44:30 -0800 (PST) Message-ID: <4f2613e50512070744p626f014esa7e23e823b0e6752@mail.gmail.com> Date: Wed, 7 Dec 2005 10:44:30 -0500 From: Zachary Adam Ozer Sender: zacharyozer@gmail.com To: 6042-probs@theory.lcs.mit.edu Subject: =?WINDOWS-1252?Q?Markov=92s_Theorem_and_Chebyshev=92s_Theorem?= 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 jB7FiV6N005151 Status: RO X-UID: 1198 Content-Length: 267 X-Keywords: NotJunk I though that both of these sections of the notes were really well done. Having read them, I really felt like I understood the concepts and I'm eager to tackle the in class problems on them. But really, I just wanted to compliment y'all on an excellent job. -zozer From fgreen@MIT.EDU Wed Dec 7 10:53:22 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 jB7FrM6N009810 for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 10:53:22 -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 jB7FrKuB004558 for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 10:53:20 -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 jB7FrDxQ021379 for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 10:53:13 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jB7FrDVV005993; Wed, 7 Dec 2005 10:53:13 -0500 Received: from FAIRCHILD-NINE-FORTY-SIX.MIT.EDU (FAIRCHILD-NINE-FORTY-SIX.MIT.EDU [18.108.5.179]) (User authenticated as fgreen@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 7 Dec 2005 10:53:13 -0500 Message-ID: <20051207105313.a4hytrdbkczk4wwo@webmail.mit.edu> Date: Wed, 7 Dec 2005 10:53:13 -0500 From: Forrest O Green To: 6042-probs@theory.csail.MIT.EDU Subject: julani, required reading comment 14, from Forrest Green 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: 1199 Content-Length: 105 X-Keywords: NotJunk I was really glad to finally figure out where variences and standerd deviations came from. -Forrest From yaser@MIT.EDU Wed Dec 7 11:03:46 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 jB7G3k6N018943 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 11:03:46 -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 jB7G3VuB018869 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 11:03:31 -0500 (EST) Received: from Charizard (NEW-THREE-TWENTY-TWO.MIT.EDU [18.241.6.67]) (authenticated bits=0) (User authenticated as ykhan@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7G3OnW026286 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 11:03:29 -0500 (EST) Message-Id: <200512071603.jB7G3OnW026286@outgoing.mit.edu> From: "Yaser Khan" To: <6042-probs@theory.lcs.mit.edu> Subject: David: tp14 reading comments Date: Wed, 7 Dec 2005 11:03:23 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0066_01C5FB1D.DAA49650" X-Mailer: Microsoft Office Outlook, Build 11.0.6353 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcX7R7/7i1tAvm00TXO1OwL8l3VbgA== X-Spam-Score: 2.779 X-Spam-Level: ** (2.779) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1200 Content-Length: 6275 X-Keywords: NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_0066_01C5FB1D.DAA49650 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Hi David, On a small point, could we use Markov instead of Chebyshev's theorem in cases where the distribution is symmetric? (As I understand that it shows the 'distance' from the mean in either direction as opposed to Markov who simply shows the deviation 'above the mean'.) My actual comment is that the proof of variance of sums seems really intimidating, I hope that the lecture & lecture slides can clear up what exactly needs to be understood about its properties. Thanks! _Yaser ------=_NextPart_000_0066_01C5FB1D.DAA49650 Content-Type: text/html; charset="us-ascii" Content-Transfer-Encoding: quoted-printable

Hi = David,

 

On a small point, could we use = Markov instead of Chebyshev’s theorem in cases where = the distribution is symmetric? (As I understand that it shows the = ‘distance’ from the mean in either direction as opposed to Markov who simply shows = the deviation ‘above the mean’.)

 

My actual comment is that the = proof of variance of sums seems really intimidating, I = hope that the lecture & lecture slides can clear up what exactly needs to = be understood about its properties.

 

Thanks!

 

_Yaser

------=_NextPart_000_0066_01C5FB1D.DAA49650-- From mitras@theory.csail.mit.edu Wed Dec 7 11:06:22 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 jB7G6M6N020704 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 11:06:22 -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 jB7G6LNj001095; Wed, 7 Dec 2005 11:06:21 -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 jB7G6CMu027472; Wed, 7 Dec 2005 11:06:13 -0500 (EST) Message-ID: <43970874.6070207@theory.csail.mit.edu> Date: Wed, 07 Dec 2005 11:06:12 -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: Andrew Shafer CC: 6042-probs@theory.csail.mit.edu Subject: Re: [Sayan] Week 14 Comments References: <000201c5f8f2$c4620760$6d04f712@ajshafer> In-Reply-To: <000201c5f8f2$c4620760$6d04f712@ajshafer> 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: 1201 Content-Length: 354 X-Keywords: NotJunk Yes. -sayan Andrew Shafer wrote: > Will we be required to know the expectation and variance for some > standard random variables? > > -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 Wed Dec 07 08:03:28 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 jB7D3R6N025170 for ; Wed, 7 Dec 2005 08:03:27 -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 1EjyxD-0003VX-GS for meyer@csail.mit.edu; Wed, 07 Dec 2005 08:03:27 -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 jB7D3QuB029979 for ; Wed, 7 Dec 2005 08:03:26 -0500 (EST) Received: from [18.194.1.37] (SN-THIRTY-SEVEN.MIT.EDU [18.194.1.37]) (authenticated bits=0) (User authenticated as petek@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7D3NpD021775 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for ; Wed, 7 Dec 2005 08:03:24 -0500 (EST) Message-ID: <4396DDAC.1050202@mit.edu> Date: Wed, 07 Dec 2005 08:03:40 -0500 From: Pete Kruskall User-Agent: Mozilla Thunderbird 1.0.7 (Windows/20050923) X-Accept-Language: en-us, en MIME-Version: 1.0 To: "Prof. Albert R. Meyer" Subject: Re: [Jelani] Markov+ Chebsnsvlskjdfslky References: <43964DE4.2020005@mit.edu> <43969BB9.2040402@csail.mit.edu> In-Reply-To: <43969BB9.2040402@csail.mit.edu> Content-Type: text/html; charset=ISO-8859-1 X-Spam-Score: 1.962 X-Scanned-By: MIMEDefang 2.42 Content-Transfer-Encoding: 7bit X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on theory.csail.mit.edu X-Spam-Level: X-Spam-Status: No, hits=-4.4 required=3.7 tests=BAYES_00,HTML_MESSAGE, HTML_TITLE_EMPTY,MIME_HTML_ONLY autolearn=no version=2.63 Status: RO Content-Length: 1718 X-UID: 1202 X-Keywords: NonJunk NotJunk Haha.   That would make more sense.  Thanks!

-P

Prof. Albert R. Meyer wrote:
if Gore got 6000 more votes, then he got 3000 ABOVE THE MEAN, and Bush got
3000 below, so the denominator should be (3000)^2.

Regards, A.

Pete Kruskall wrote:

> Despite the fact that my eyes / brain refuse to take the effort to actually pronounce the second man's name, I got through this week's notes in an ok manner.  I'm having trouble getting the last TP prob right.  Given standard dev = 2000, and you want the pr that gore gets 6,000 more votes, shouldn't the prob be bounded by (standard dev)^2 / (6,000)^2  =  1/9?  >
> Also, this week's notes is a good example of stuff that rather than make a good home in my head will probably make a much better one on the crib sheet we bring into the exam.
>
> -P
>
>--  >Pete Kruskall
>28 The Fenway
>Boston, MA 02215
>
>:::::::::::::::::::::::::::::
>508.843.5861 ::::Cell Phone::
>617.536.9925 :::Sigma Nu:::::
> 


-- 
Pete Kruskall
28 The Fenway
Boston, MA 02215

:::::::::::::::::::::::::::::
508.843.5861 ::::Cell Phone::
617.536.9925 :::Sigma Nu:::::
From hmzhou@blackbird.csail.mit.edu Wed Dec 7 11:12:09 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 jB7GC96N023451; Wed, 7 Dec 2005 11:12:09 -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 jB7GC8B1025648; Wed, 7 Dec 2005 11:12:08 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jB7GC8Kr025645; Wed, 7 Dec 2005 11:12:08 -0500 Date: Wed, 7 Dec 2005 11:12:07 -0500 (EST) From: Hanson Zhou To: Alex Valys cc: 6042-probs@theory.lcs.mit.edu Subject: Re: 6.042: [Hanson] Required Reading Comments In-Reply-To: <2C7AD70A-F06B-4655-8E53-8759C266EA5D@mit.edu> Message-ID: References: <2C7AD70A-F06B-4655-8E53-8759C266EA5D@mit.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1203 Content-Length: 309 X-Keywords: NonJunk NotJunk It shows you an example on page 9...you simply use definition of expectation. -Hanson On Wed, 7 Dec 2005, Alex Valys wrote: > I am a little unclear about how to use the alternative expression of > variance described in section 8.2 (page 8). How is one supposed to > find the value of E[R^2]? > > Alex > > From alisonc@MIT.EDU Wed Dec 7 11:13:35 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 jB7GDZ6N023629 for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 11:13:35 -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 jB7GDXoV027679 for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 11:13:33 -0500 (EST) Received: from sns23.mit.edu (SNS23.MIT.EDU [18.62.2.196]) (authenticated bits=56) (User authenticated as alisonc@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7GDV46000744 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 11:13:31 -0500 (EST) Received: (from alisonc@localhost) by sns23.mit.edu (8.12.9) id jB7GDVjm007524; Wed, 7 Dec 2005 11:13:31 -0500 Subject: [Hanson] comments on notes #14 From: Alison S Cichowlas To: 6042-probs@theory.csail.MIT.EDU Content-Type: text/plain Content-Transfer-Encoding: 7bit Date: Wed, 07 Dec 2005 11:13:30 -0500 Message-Id: <1133972010.7478.0.camel@sns23.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: 1204 Content-Length: 96 X-Keywords: NotJunk I found the section on variance sort of confusing -- more examples would have been really nice. From dshin@MIT.EDU Wed Dec 7 11:13:46 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 jB7GDj6N023636 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 11:13:45 -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 jB7GDiNj001539; Wed, 7 Dec 2005 11:13:44 -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 jB7GDaok012628; Wed, 7 Dec 2005 11:13:37 -0500 (EST) Message-ID: <43970A0F.8040800@mit.edu> Date: Wed, 07 Dec 2005 11:13:03 -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: <1133967691.21236.9.camel@m12-182-19.mit.edu> In-Reply-To: <1133967691.21236.9.camel@m12-182-19.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 3.263 X-Spam-Level: *** (3.263) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1205 Content-Length: 996 X-Keywords: NotJunk There is no clean formula for E[max{A,B}] given E[A] and E[B]. One of the in-class problems actually outlined a nice way to compute E[max{k independent die}] - it used the formula E[X] = \sum_i Pr[X>i] DS Katherine Romer wrote: >"the expected value of a sum of random variables is the sum of the >expected values of the variables" (p. 1) > >When we consider two random variables at the same time, I understand how >we get the expectation of their sum, but how do we expect the values of >the variables to be distributed? For example, say we're rolling two >six-sided dice. We expect them to sum to 7, and each die individualy has >an expected value of 3.5. Is the expected maximum of the dice 3.5, >because that's the expectation of each die? It seems likely that one die >would have a higher value than the other on most rolls, so it seems that >the expected maximum must be larger than 3.5 and the expected minimum >must be less--how would you go about computing this? > >Katherine > > From mitras@theory.csail.mit.edu Wed Dec 7 11:16:22 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 jB7GGM6N023996 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 11:16:22 -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 jB7GGKNj001682; Wed, 7 Dec 2005 11:16:20 -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 jB7GGGMu028185; Wed, 7 Dec 2005 11:16:16 -0500 (EST) Message-ID: <43970AD0.6010503@theory.csail.mit.edu> Date: Wed, 07 Dec 2005 11:16:16 -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: Isaac Charny CC: 6042-probs@theory.csail.mit.edu Subject: Re: [Sayan] Week 14 Comments References: <4394F6C5.7040907@mit.edu> In-Reply-To: <4394F6C5.7040907@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: 1206 Content-Length: 296 X-Keywords: NotJunk Hope you'll attend today's lecture. An easy way to calculate variance is to use theorem 8.1, i.e., Var(X) = E(X^2) - (E(X))^2. -sayan Isaac Charny wrote: > I don't really understand variance, what it is, and how to quickly > calculate it. Please cover this in the next lecture. > > ~Isaac > From crowell@MIT.EDU Wed Dec 7 11:17:08 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 jB7GH86N024096 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:17:08 -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 jB7GH7oV002420 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:17:07 -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 jB7GH59a002209 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:17:06 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jB7GH5wM018129; Wed, 7 Dec 2005 11:17:05 -0500 Received: from SNS25.MIT.EDU (SNS25.MIT.EDU [18.62.2.198]) (User authenticated as crowell@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 7 Dec 2005 11:17:05 -0500 Message-ID: <20051207111705.6ltzed48owdck8w0@webmail.mit.edu> Date: Wed, 7 Dec 2005 11:17:05 -0500 From: Robert Crowell To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] 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: 1207 Content-Length: 155 X-Keywords: NonJunk NotJunk I really found the examples (coupon collector etc) to be very interesting. These were talked about in lecture and are on 1.3 on page 3. -Rob Crowell From kktyan@MIT.EDU Wed Dec 7 11:18:57 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 jB7GIu6N024182 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:18:56 -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 jB7GItoV004761 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:18:55 -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 jB7GIqRZ002989 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:18:52 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-5.mit.edu (8.12.4) id jB7GIq0K019874; Wed, 7 Dec 2005 11:18:52 -0500 Received: from BURTON-THREE-SEVENTY.MIT.EDU (BURTON-THREE-SEVENTY.MIT.EDU [18.247.6.115]) (User authenticated as kktyan@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 7 Dec 2005 11:18:52 -0500 Message-ID: <20051207111852.p9kr5f3649jkckwk@webmail.mit.edu> Date: Wed, 7 Dec 2005 11:18:52 -0500 From: Karena Tyan To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] Reading Comments 14 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: 1208 Content-Length: 527 X-Keywords: NonJunk NotJunk I was a little confused over the definition of variance on page 13. Var[R]::= E[(R - E[R])^2] makes it seem as if it's the expected value of the squares of (R - E[R]), so I thought this meant calculating the sums of the squares and dividing by the probability of each happening. It seems to be more like the square of the expected (R - E[R]) and then the expected value of that...or something. In other words, I'm confused over the definition of variance. - Karena -- 410 Memorial Drive Cambridge, MA 02139 (585)957-5923 From dshin@MIT.EDU Wed Dec 7 11:27:25 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 jB7GRO6N028629 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 11:27:25 -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 jB7GRN7T014711 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 11:27:23 -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 jB7GRNd9000122; Wed, 7 Dec 2005 11:27:23 -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 jB7GRKMu029003; Wed, 7 Dec 2005 11:27:21 -0500 (EST) Message-ID: <43970D48.9030300@mit.edu> Date: Wed, 07 Dec 2005 11:26:48 -0500 From: David Shin User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Jason Juang CC: 6042-probs@theory.lcs.mit.edu Subject: Re: [David] Week 14 Comments References: <43926B8E.9080106@mit.edu> In-Reply-To: <43926B8E.9080106@mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 3.263 X-Spam-Level: *** (3.263) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1209 Content-Length: 487 X-Keywords: NotJunk Heh, Professor Meyer and I discussed this after class the other day. Were you able to solve it during the exam? DS Jason Juang wrote: > I don't have much comment on the reading, so I'll instead mention that > Problem B4 on the Putnam today was, paraphrased: > Let f(m,n) be the number of n-tuples of integers (x_1, x_2, ..., > x_n) which satisfy |x_1| + |x_2| + ... + |x_n| <= m. Show that f(m,n) > = f(n,m). > > ... Sounds like a good final exam question to me ;) > > Jason. From mitras@theory.csail.mit.edu Wed Dec 7 11:27:26 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 jB7GRQ6N028634 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:27:26 -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 jB7GRP7T014734 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:27:25 -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 jB7GLcd9029809; Wed, 7 Dec 2005 11:21:39 -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 jB7GLVMu028657; Wed, 7 Dec 2005 11:21:31 -0500 (EST) Message-ID: <43970C0B.3030400@theory.csail.mit.edu> Date: Wed, 07 Dec 2005 11:21:31 -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: Svetlana Goldenberg CC: 6042-probs@theory.lcs.MIT.EDU Subject: Re: [Sayan] TP14 References: <20051207034106.2sfpeg8bro08co80@webmail.mit.edu> In-Reply-To: <20051207034106.2sfpeg8bro08co80@webmail.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: 1210 Content-Length: 412 X-Keywords: NotJunk By alternative definition I guess you mean theorem 8.1, right ? This also happens to be an easier definition to use when you are computing variance. -Sayan Svetlana Goldenberg wrote: >The part that I found to be the most intriguing was the symmetry in the >alternative definition of variance, particularly because the link between the >original definition and this version is far from intuitive. >Lana > > From dshin@MIT.EDU Wed Dec 7 11:27:27 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 jB7GRR6N028639 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 11:27:27 -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 jB7GRP7V014735 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 11:27:26 -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 jB7GQNd9000071; Wed, 7 Dec 2005 11:26:23 -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 jB7GQLok013415; Wed, 7 Dec 2005 11:26:21 -0500 (EST) Message-ID: <43970D0C.9010302@mit.edu> Date: Wed, 07 Dec 2005 11:25:48 -0500 From: David Shin User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Steven Zhou CC: 6042-probs@theory.lcs.mit.edu Subject: Re: [David] tp-14 References: <5.2.1.1.2.20051207003858.02aa40a0@po9.mit.edu> In-Reply-To: <5.2.1.1.2.20051207003858.02aa40a0@po9.mit.edu> 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: 1211 Content-Length: 460 X-Keywords: NotJunk In fact, it should be something even more complicated than a quadratic. As a hint, you will need to use the approximation ln(1+x)=x to get a closed form. DS Steven Zhou wrote: > Hi, > > Topic is clear. I have a question for problem set number 5. With the > answer i got for (a), if i were to solve for K that minimized that > expression, I get a quadratic equation. Is it that complicated, or > did I do part (a) wrong. Thanks. > > - Steven Zhou > From hmzhou@blackbird.csail.mit.edu Wed Dec 7 11:27:54 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 jB7GRs6N028720; Wed, 7 Dec 2005 11:27:54 -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 jB7GRsLi025795; Wed, 7 Dec 2005 11:27:54 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jB7GRsrl025792; Wed, 7 Dec 2005 11:27:54 -0500 Date: Wed, 7 Dec 2005 11:27:53 -0500 (EST) From: Hanson Zhou To: Karena Tyan cc: 6042-probs@theory.lcs.MIT.EDU Subject: Re: [Hanson] Reading Comments 14 In-Reply-To: <20051207111852.p9kr5f3649jkckwk@webmail.mit.edu> Message-ID: References: <20051207111852.p9kr5f3649jkckwk@webmail.mit.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1212 Content-Length: 853 X-Keywords: NonJunk NotJunk Hmm...not sure what the question is here. Maybe it would help if you looked at it like this: Var[R] = E[(R-c)^2], for a constant c=E[R]. Now we are talking about essentially the expectation of the square of a random variable. Does that make sense? -Hanson On Wed, 7 Dec 2005, Karena Tyan wrote: > I was a little confused over the definition of variance on page 13. > > Var[R]::= E[(R - E[R])^2] makes it seem as if it's the expected value of > the squares of (R - E[R]), so I thought this meant calculating the sums > of the squares and dividing by the probability of each happening. It > seems to be more like the square of the expected (R - E[R]) and then the > expected value of that...or something. In other words, I'm confused > over the definition of variance. > > - Karena > > -- 410 Memorial Drive Cambridge, MA 02139 (585)957-5923 > From dshin@MIT.EDU Wed Dec 7 11:29:09 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 jB7GT96N029063 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 11:29:09 -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 jB7GT7Nj002403; Wed, 7 Dec 2005 11:29:07 -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 jB7GSwMu029086; Wed, 7 Dec 2005 11:28:59 -0500 (EST) Message-ID: <43970DA9.1010004@mit.edu> Date: Wed, 07 Dec 2005 11:28:25 -0500 From: David Shin User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Harrison King Hall CC: 6042-probs@theory.csail.mit.edu Subject: Re: [David] Week 14 Comments References: <24b9be0d51a5c9b1398b83895ce0c687@mit.edu> In-Reply-To: <24b9be0d51a5c9b1398b83895ce0c687@mit.edu> 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: 1213 Content-Length: 889 X-Keywords: NotJunk Harrison King Hall wrote: > David- > Even after our talk today I still had trouble with variance and using > it to apply Chebyshev's theorem. For that matter is is taking me a > long time to figure out Markov's as well. I think that I will get it > by the time we go over it in class. I think that my problem lies in > the fact that I don't really get E[R-c] where R is a random variable > and c is some constant. I think this can be explained by linearity of > expectation and E[c]=c, but I am not sure. Yes, thats exactly right - that's why E[R-c] = E[R] - E[c] = E[R] - c. > Well, that is all I have to say, but I need to tell you that there is > a high probability that I will not be in class on Friday since I have > an away swim meet. I will get back to you on the exact time that I > will be leaving and whether it means I will miss class. No prob. > -Harrison > From mitras@theory.csail.mit.edu Wed Dec 7 11:29:53 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 jB7GTr6N030561 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 11:29:53 -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 jB7GTq7T018838 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 11:29:52 -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 jB7GTpd9000254; Wed, 7 Dec 2005 11:29:52 -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 jB7GThok013631; Wed, 7 Dec 2005 11:29:44 -0500 (EST) Message-ID: <43970DF7.6050106@theory.csail.mit.edu> Date: Wed, 07 Dec 2005 11:29:43 -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 14 Comments References: <6.2.1.2.2.20051207001238.01f2fe20@po12.mit.edu> In-Reply-To: <6.2.1.2.2.20051207001238.01f2fe20@po12.mit.edu> 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: 1214 Content-Length: 819 X-Keywords: NotJunk Hi Praveen, Var[X_i] is calculated usinf theorem 8.1 which says that Var[X_i] = E[X_i^2] - (E[X_i])^2. E[X_i] = 1 x1/2 + 0 = 1/2 (E[X_i])^2 = 1/4 E[X_i^2] = 1^2 x 1/2 + 0 = 1/2 So, Var[X_i] = 1/2 - 1/4 =1/4. -sayan Praveen Pamidimukkala wrote: > Hi, > > My question pertains to the TP as opposed to the reading. In TP.14.3, > it reads: > > > "Suppose you flip a fair coin 100 times. The coin flips are all > mutually independent. > > 3. What is the variance of the number of heads? > > Let Xi be the random variable whose value is 1 if the ith coin flip is > heads. Then > Var[Xi] = 1/2 - (1/2)2 = 1/4. So Var[X1 + ... + X100] = 100·(1/4) = 25. > (Note we can use additivity of variance here since our flips are > independent.) ] " > > I don't understand the calculation for Var[Xi]. > > Thanks, > Praveen > From sil_03@MIT.EDU Wed Dec 7 11:35:17 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 jB7GZH6N001383 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:35:17 -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 jB7GXppL025487 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:35:16 -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 jB7G4Fg5026664 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 11:04:15 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jB7G4FU7016024; Wed, 7 Dec 2005 11:04:15 -0500 Received: from NEW-ONE-TWENTY-ONE.MIT.EDU (NEW-ONE-TWENTY-ONE.MIT.EDU [18.241.5.121]) (User authenticated as sil_03@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 7 Dec 2005 11:04:15 -0500 Message-ID: <20051207110415.ct97lpsjz3wcskoc@webmail.mit.edu> Date: Wed, 7 Dec 2005 11:04:15 -0500 From: "Silvia F. Baptista" To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] week 14 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: 1215 Content-Length: 111 X-Keywords: NotJunk I'm confused about the Markov and Chebyshev upper bounds. Especially when you're given a lower bound. Silvia From aston@MIT.EDU Wed Dec 7 11:38:21 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 jB7GcL6N001562 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 11:38:21 -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 jB7GcKoV001842 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 11:38:20 -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 jB7GcB4Z011759 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 11:38:11 -0500 (EST) Message-Id: <200512071638.jB7GcB4Z011759@outgoing.mit.edu> From: "Aston Motes" To: <6042-probs@theory.csail.mit.edu> Subject: [Hanson] Week 14 Comments Date: Wed, 7 Dec 2005 11:38:08 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0000_01C5FB22.B3276350" X-Mailer: Microsoft Office Outlook, Build 11.0.6353 Thread-Index: AcX7TJpQoe53F9VkTxS7Xxt+0iciRg== X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: 2.038 X-Spam-Level: ** (2.038) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1216 Content-Length: 2884 X-Keywords: NotJunk This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C5FB22.B3276350 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit I had an oddly intuitive sense of Markov's theorem as far as the online questions went, though I realized once I saw the formula for it that I didn't really understand why what I was doing worked. The explanation is pretty nice (on pages 10 and 11). I was wondering, though, if there's some way to tell how well the Markov bound actually bounds examples. Is it due to the variance? - Aston ------=_NextPart_000_0000_01C5FB22.B3276350 Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: quoted-printable

I had an oddly intuitive sense of Markov’s = theorem as far as the online questions went, though I realized once I saw the = formula for it that I didn’t really understand why what I was doing worked. = The explanation is pretty nice (on pages 10 and 11). =

 

I was wondering, though, if there’s some way to = tell how well the Markov bound actually bounds examples. Is it due to the = variance?

 

         =    - Aston

------=_NextPart_000_0000_01C5FB22.B3276350-- From ozcan@MIT.EDU Wed Dec 7 12:09:04 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 jB7H946N022813 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 12:09:04 -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 jB7H93Nj004624 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 12:09:03 -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 jB7H8tol016374 for <6042-probs@theory.csail.mit.edu>; Wed, 7 Dec 2005 12:08:55 -0500 (EST) Message-Id: <5.2.1.1.2.20051207120612.02175200@po12.mit.edu> X-Sender: ozcan@hesiod (Unverified) X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 07 Dec 2005 12:08:51 -0500 To: 6042-probs@theory.csail.mit.edu From: Yasin Ozcan 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: 1217 Content-Length: 133 X-Keywords: Section 3, Conditional Expectation, Theorem 3.4 This is an amazing way of finding the expectation for pair-wise disjoint events. From jstritar@MIT.EDU Wed Dec 7 12:25:02 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 jB7HP26N031269 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 12:25:02 -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 jB7HP0oV004642 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 12:25:00 -0500 (EST) Received: from JSTRITAR.MIT.EDU (JSTRITAR.MIT.EDU [18.245.4.29]) (authenticated bits=0) (User authenticated as jstritar@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7HOq3T003023 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 12:24:53 -0500 (EST) Subject: [Sayan] Reading comments From: Jon Stritar To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Wed, 07 Dec 2005 12:25:19 -0500 Message-Id: <1133976319.1652.3.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: 1218 Content-Length: 339 X-Keywords: NonJunk Sorry for being a bit late... I actually did the reading/TP on Monday and forgot to send the email. 3. Conditional Expectation I like the law of total expectation. It seems like it usually comes in very handy. I feel like you might be able to make some cool AI using some sort of conditional expectations + bayesian probabilities. Jon From meyer@imap.theory.csail.mit.edu Wed Dec 07 10:56:59 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 jB7Fuu6N014313 for <6.042-online-tutor@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:56:56 -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 jB7FutuB009231 for <6.042-online-tutor@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:56:55 -0500 (EST) Received: from [18.244.7.131] (SENIOR-SIX-FOURTY-TWO.MIT.EDU [18.244.7.131]) (authenticated bits=0) (User authenticated as rshearer@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7FulJr023080 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6.042-online-tutor@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:56:48 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v623) Content-Transfer-Encoding: 7bit Message-Id: <18f0f87df9571f2bca682ae228610a93@mit.edu> Content-Type: text/plain; charset=US-ASCII; format=flowed To: 6.042-online-tutor@theory.csail.mit.edu From: Rachel Shearer Subject: [Jelani] This Week's Comment Date: Wed, 7 Dec 2005 10:56:41 -0500 X-Mailer: Apple Mail (2.623) 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=BAYES_00 autolearn=ham version=2.63 Status: RO Content-Length: 96 X-UID: 1219 X-Keywords: NonJunk I don't really understand the standard deviation stuff. Lecture should help, I think. Rachel From nedzel@MIT.EDU Wed Dec 7 13:35:18 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 jB7IZI6N001225 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 7 Dec 2005 13:35:18 -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 jB7IZFoV005029; Wed, 7 Dec 2005 13:35:15 -0500 (EST) Received: from m38-370-5.mit.edu (M38-370-5.MIT.EDU [18.107.0.24]) (authenticated bits=56) (User authenticated as nedzel@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7IZ8cK000862 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT); Wed, 7 Dec 2005 13:35:08 -0500 (EST) Received: (from nedzel@localhost) by m38-370-5.mit.edu (8.12.9) id jB7IZ7An010815; Wed, 7 Dec 2005 13:35:07 -0500 Subject: [Sayan] Week 14 Comments From: David A Nedzel To: 6042-probs@theory.lcs.MIT.EDU Content-Type: text/plain Content-Transfer-Encoding: 7bit Date: Wed, 07 Dec 2005 13:35:07 -0500 Message-Id: <1133980507.10767.1.camel@m38-370-5.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: 1220 Content-Length: 118 X-Keywords: NonJunk What is the significance of Markov and Chebyshev error bounds as they relate to statistical sampling theory? - David From dangut@MIT.EDU Wed Dec 7 13:44:43 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 jB7Iih6N014728 for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 13:44:43 -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 jB7IifoV017055 for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 13:44:41 -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 jB7IiYhO004847 for <6042-probs@theory.csail.MIT.EDU>; Wed, 7 Dec 2005 13:44:34 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jB7IiYX8009097; Wed, 7 Dec 2005 13:44:34 -0500 Received: from MAJI.MIT.EDU (MAJI.MIT.EDU [18.239.1.17]) (User authenticated as dangut@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 7 Dec 2005 13:44:34 -0500 Message-ID: <20051207134434.80w3lpulfndwk8os@webmail.mit.edu> Date: Wed, 7 Dec 2005 13:44:34 -0500 From: Daniel A Gutierrez To: 6042-probs@theory.csail.MIT.EDU Subject: [Hansen] TP 14 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: 1221 Content-Length: 134 X-Keywords: NonJunk I'm still a little confused, is variance related to independence? Does independence necessarily imply normal probability of variance? From pjs@MIT.EDU Wed Dec 7 15:37:24 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 jB7KbO6N027614 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 15:37:24 -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 jB7KbMqY015947 for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 15:37:22 -0500 (EST) Received: from [18.24.1.245] (24-1-245.dynamic.csail.mit.edu [18.24.1.245]) (authenticated bits=0) (User authenticated as pjs@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7KbAbr024969 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 7 Dec 2005 15:37:16 -0500 (EST) Message-ID: <439747F4.3080403@mit.edu> Date: Wed, 07 Dec 2005 15:37:08 -0500 From: PJ Steiner User-Agent: Mozilla Thunderbird 1.0.7 (X11/20051130) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [Sayan] reading comments 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: 1222 Content-Length: 90 X-Keywords: NonJunk I found the distinction between pairwise independence and independence interesting. pjs From meyer@imap.theory.csail.mit.edu Wed Dec 07 10:56:56 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 jB7Fuu6N014313 for <6.042-online-tutor@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:56:56 -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 jB7FutuB009231 for <6.042-online-tutor@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:56:55 -0500 (EST) Received: from [18.244.7.131] (SENIOR-SIX-FOURTY-TWO.MIT.EDU [18.244.7.131]) (authenticated bits=0) (User authenticated as rshearer@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jB7FulJr023080 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6.042-online-tutor@theory.csail.mit.edu>; Wed, 7 Dec 2005 10:56:48 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v623) Content-Transfer-Encoding: 7bit Message-Id: <18f0f87df9571f2bca682ae228610a93@mit.edu> Content-Type: text/plain; charset=US-ASCII; format=flowed To: 6.042-online-tutor@theory.csail.mit.edu From: Rachel Shearer Subject: [Jelani] This Week's Comment Date: Wed, 7 Dec 2005 10:56:41 -0500 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 Content-Length: 97 X-UID: 1224 X-Keywords: NonJunk NotJunk I don't really understand the standard deviation stuff. Lecture should help, I think. Rachel