From meyer@imap.theory.csail.mit.edu Tue Nov 22 10:03:59 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 jAMF3x5o007180 for ; Tue, 22 Nov 2005 10:03:59 -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 1EeZgc-0007G0-TK for meyer@csail.MIT.EDU; Tue, 22 Nov 2005 10:03:58 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAMF3vKG001895 for ; Tue, 22 Nov 2005 10:03:57 -0500 (EST) Received: from no-knife.mit.edu (NO-KNIFE.MIT.EDU [18.7.16.64]) (authenticated bits=56) (User authenticated as hmzhou@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAMF3mQT010247 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for ; Tue, 22 Nov 2005 10:03:51 -0500 (EST) Received: (from hmzhou@localhost) by no-knife.mit.edu (8.12.9) id jAMF3mQe004898; Tue, 22 Nov 2005 10:03:48 -0500 (EST) Date: Tue, 22 Nov 2005 10:03:48 -0500 (EST) From: Hanson M Zhou To: meyer@csail.MIT.EDU Subject: reading comment (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Spam-Score: -2.599 X-Scanned-By: MIMEDefang 2.42 X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on theory.csail.mit.edu X-Spam-Level: X-Spam-Status: No, hits=-4.9 required=3.7 tests=AWL,BAYES_00 autolearn=ham version=2.63 Status: RO Content-Length: 543 X-IMAPbase: 1126748715 1045 NonJunk $Label4 $Label1 $Label2 $Label3 $Label5 Junk $MDNSent $Forwarded NotJunk X-UID: 969 X-Status: A X-Keywords: $Forwarded Elizabeth Reid's comments below. Might just be something with email in general today. -Hanson ---------- Forwarded message ---------- Date: Tue, 22 Nov 2005 04:19:34 -0500 From: Elizabeth Reid To: Hanson Zhou Subject: reading comment I sent a reading comment in via the 6042-probs mailing list, but I got a weird error message, so I figured I'd send it directly to you, just in case. Anyway, the a posteriori problems were a bit odd, but I think I get the idea behind them now. Elizabeth From shauni@MIT.EDU Tue Nov 22 14:19:18 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 jAMJJI5o014065 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 14:19:18 -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 jAMJJHLH027143 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 14:19:17 -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 jAMJJFvL029203 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 14:19:15 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jAMJJFEU011572; Tue, 22 Nov 2005 14:19:15 -0500 Received: from WOMENS-STUDIES.MIT.EDU (WOMENS-STUDIES.MIT.EDU [18.51.0.243]) (User authenticated as shauni@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 22 Nov 2005 14:19:15 -0500 Message-ID: <20051122141915.qvcizm6yhtgkwook@webmail.mit.edu> Date: Tue, 22 Nov 2005 14:19:15 -0500 From: "I. Shauni Deshmukh" To: 6042-probs@theory.lcs.MIT.EDU Subject: [Sayan] week 12 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: 971 Content-Length: 75 X-Keywords: NotJunk I would like to see more explanation/examples with infinite sample spaces. From pgroudas@MIT.EDU Tue Nov 22 14:53:38 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 jAMJrc5o031991 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 14:53:38 -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 jAMJraLH010115 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 14:53:37 -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 jAMJrUQF015047 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 14:53:30 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-4.mit.edu (8.12.4) id jAMJrU9E011751; Tue, 22 Nov 2005 14:53:30 -0500 Received: from 18.233.0.185 ([18.233.0.185]) (User authenticated as pgroudas@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 22 Nov 2005 14:53:30 -0500 Message-ID: <20051122145330.b2djqwd3utgk8w0c@webmail.mit.edu> Date: Tue, 22 Nov 2005 14:53:30 -0500 From: Paul Groudas To: 6042-probs@theory.lcs.MIT.EDU Subject: [HANSON] Week 12 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: 972 Content-Length: 245 X-Keywords: NotJunk I found the reading fairly straightforward, although the last example about mutual vs. pairwise independence could have been explained further. I'm just not exactly grasping how the calculation drops from 1 in 170 million to 1 in 17000. -Paul From bakster@MIT.EDU Tue Nov 22 15:50:22 2005 Return-Path: Received: from bexxxley.mit.edu (BEXXXLEY.MIT.EDU [18.246.1.238]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAMKoM5o024709 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 15:50:22 -0500 Received: (from bakster@localhost) by bexxxley.mit.edu (8.12.9) id jAMKoM2Q014134; Tue, 22 Nov 2005 15:50:22 -0500 Date: Tue, 22 Nov 2005 15:50:22 -0500 (EST) From: Alexander G Bakst X-X-Sender: bakster@bexxxley To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] Lecture Notes 12 Comments Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 973 Content-Length: 140 X-Keywords: NotJunk The coin problem example from the lecture notes confused me. Could you explain it a little? Or can we cover it in class? Alexander Bakst From ajshafer@MIT.EDU Tue Nov 22 15:58:13 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 jAMKwD5o029233 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 15:58:13 -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 jAMKwCLH022858 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 15:58:12 -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 jAMKw4e8014406 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 15:58:04 -0500 (EST) Message-ID: <004601c5efa7$715b4170$6d04f712@ajshafer> From: "Andrew Shafer" To: <6042-probs@theory.csail.mit.edu> Subject: [Sayan] Week 12 Comments Date: Tue, 22 Nov 2005 15:58:08 -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: 974 Content-Length: 262 X-Keywords: NotJunk Will many of our problems be dealing with infinite trees? -Andrew ---------------------------- Illegitmitatum Non Carborundum Est Andrew Shafer, MIT Blog http://shaferandrew.blogspot.com Si hoc legere scis numium eruditionis habes. ---------------------------- From dangut@MIT.EDU Tue Nov 22 17:33:03 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 jAMMX35o031688 for <6042-probs@theory.csail.MIT.EDU>; Tue, 22 Nov 2005 17:33:03 -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 jAMMX1L7026270 for <6042-probs@theory.csail.MIT.EDU>; Tue, 22 Nov 2005 17:33:02 -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 jAMMWx18019923 for <6042-probs@theory.csail.MIT.EDU>; Tue, 22 Nov 2005 17:33:00 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-4.mit.edu (8.12.4) id jAMMWxBw003186; Tue, 22 Nov 2005 17:32:59 -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 ; Tue, 22 Nov 2005 17:32:59 -0500 Message-ID: <20051122173259.dw4rq0gjg9c8cg0k@webmail.mit.edu> Date: Tue, 22 Nov 2005 17:32:59 -0500 From: Daniel A Gutierrez To: 6042-probs@theory.csail.MIT.EDU Subject: [Hanson] Probability reading response MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 975 Content-Length: 408 X-Keywords: NotJunk This is all fairly straight forward. I guess the only thing I haven't really seen before and would like to see in class is probability as variables appproach infinity (I have seen some funny proofs before that sound illogical,but become logical when carried to infinite, such as the odds out of any number possible of picking a number divisible by 11 is zero? or maybe it was just a false proof...) -Daniel From kjhollen@mit.edu Tue Nov 22 18:27:50 2005 Return-Path: Received: from takanawa.isao.net (fi01-84CBc5.tokyo.flets.isao.net [211.132.203.197]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAMNRn5o026574 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 18:27:50 -0500 Received: from [172.16.0.19] (unknown [172.16.0.19]) by takanawa.isao.net (Postfix) with ESMTP id 819023798 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 08:27:43 +0900 (JST) Subject: [Hanson] a posteriori probabilities From: Kate Hollenbach To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Tue, 22 Nov 2005 18:27:42 -0500 Message-Id: <1132702062.7874.1.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.4.1 Content-Transfer-Encoding: 7bit Status: RO X-UID: 976 Content-Length: 114 X-Keywords: NotJunk i found this section in the reading (p. 18) to be a bit confusing. it would be helpful to go over it in lecture. From vixen@MIT.EDU Tue Nov 22 18:40:33 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAMNeX5o003166 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 18:40:33 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAMNeWL7015735 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 18:40:32 -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 jAMNePHj005681 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 18:40:26 -0500 (EST) Mime-Version: 1.0 X-Sender: vixen@hesiod Message-Id: Date: Tue, 22 Nov 2005 18:38:18 -0500 To: 6042-probs@theory.lcs.mit.edu From: Amanda Seybold Subject: LN12 Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Spam-Score: 3.076 X-Spam-Level: *** (3.076) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 977 Content-Length: 56 X-Keywords: I was confused by the section on pairwise independence. From hzhou@MIT.EDU Tue Nov 22 19:21:29 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 jAN0LT5o028829 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 19:21:29 -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 jAN0LRL7013609 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 19:21:27 -0500 (EST) Received: from hzhou.mit.edu (BURTON-SEVENTY-ONE.MIT.EDU [18.247.5.71]) (authenticated bits=0) (User authenticated as hzhou@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN0LKid012409 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 19:21:21 -0500 (EST) Message-Id: <5.2.1.1.2.20051122192047.02b05dd8@po9.mit.edu> X-Sender: hzhou@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Tue, 22 Nov 2005 19:21:25 -0500 To: 6042-probs@theory.lcs.mit.edu From: Steven Zhou Subject: David-tp12 reading comment Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 978 Content-Length: 160 X-Keywords: NonJunk Hey, Nothing too confusing. Independence is a bit tricky, but I guess its easy to be determined if you just do the conditional probability. - steven zhou From hectorb@MIT.EDU Tue Nov 22 19:26:44 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAN0Qi5o029322 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 19:26:44 -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 jAN0QfL7017154; Tue, 22 Nov 2005 19:26:42 -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 jAN0QYF1013200 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT); Tue, 22 Nov 2005 19:26:35 -0500 (EST) Message-ID: <4383B739.1060300@mit.edu> Date: Tue, 22 Nov 2005 19:26:33 -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 12 Reading Comments Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 2.706 X-Spam-Level: ** (2.706) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 979 Content-Length: 278 X-Keywords: NonJunk "The three events A1, A2, and A3 are not mutually independent, even though all pairs of events are independent!" p.26 I found independence to be the hardest topic to understand. Distinguishing different types of independence is tricky. Probability itself is tricky. -Hector From rshroff@MIT.EDU Tue Nov 22 19:42:39 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAN0gd5o008829 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 19:42:39 -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 jAN0gcL7027754 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 19:42:38 -0500 (EST) Received: from w92-130-webmail-1.mit.edu (W92-130-WEBMAIL-1.MIT.EDU [18.7.22.131]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN0gV8E015625 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 19:42:31 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-1.mit.edu (8.12.4) id jAN0gVot019137; Tue, 22 Nov 2005 19:42:31 -0500 Received: from NEXT-THREE-EIGHTY-TWO.MIT.EDU (NEXT-THREE-EIGHTY-TWO.MIT.EDU [18.242.6.127]) (User authenticated as rshroff@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 22 Nov 2005 19:42:31 -0500 Message-ID: <20051122194231.tbchecdfkkhwoc8w@webmail.mit.edu> Date: Tue, 22 Nov 2005 19:42:31 -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: 980 Content-Length: 164 X-Keywords: NonJunk I realy enjoyeed the reading. I am currently also taking 6.041 so it was intersting to see the material taught in a somewhat different perspective. -Rahul Shroff From yangc@MIT.EDU Tue Nov 22 20:17:14 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 jAN1HD5o021808 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 20:17:14 -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 jAN1HCBV021210 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 20:17:12 -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 jAN1H4mA021113 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 20:17:05 -0500 (EST) Message-Id: <200511230117.jAN1H4mA021113@outgoing.mit.edu> From: "Chris Yang" To: <6042-probs@theory.csail.mit.edu> Subject: [David] Week 12 Comments Date: Tue, 22 Nov 2005 20:18:54 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_00EE_01C5EFA1.F6B94FC0" X-Mailer: Microsoft Office Outlook, Build 11.0.5510 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcXvy97Os6BNr2WpSvSo3mINGkUcnQ== X-Spam-Score: 1.668 X-Spam-Level: * (1.668) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 981 Content-Length: 2913 X-Keywords: NonJunk This is a multi-part message in MIME format. ------=_NextPart_000_00EE_01C5EFA1.F6B94FC0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Quick question regarding conditional probability: is asking the probability of something given another event the same as the probability of that something happening using all the probabilities on the subtree after that "another" event? Hm, that is a difficult question to ask in e-mail form. Assuming an event is given - is that equivalent to, say, traversing down one path on the tree of that given event? Have a good break! -Chris Yang ------=_NextPart_000_00EE_01C5EFA1.F6B94FC0 Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: quoted-printable

Quick question regarding conditional = probability:  is asking the probability of something given another event the same as the probability of that something happening using all the probabilities on = the subtree after that “another” event?  Hm, that is a = difficult question to ask in e-mail form.  Assuming an event is given – = is that equivalent to, say, traversing down one path on the tree of that given = event?

 

Have a good break!

 

-Chris Yang

------=_NextPart_000_00EE_01C5EFA1.F6B94FC0-- From xiaoranz@MIT.EDU Tue Nov 22 20:24:25 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAN1OP5o026687 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 20:24:25 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAN1ONBV026108 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 20:24:24 -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 jAN1OH5O022232 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 20:24:17 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jAN1OH9e026508; Tue, 22 Nov 2005 20:24:17 -0500 Received: from MCCORMICK-SEVEN-SIXTY.MIT.EDU (MCCORMICK-SEVEN-SIXTY.MIT.EDU [18.240.7.249]) (User authenticated as xiaoranz@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 22 Nov 2005 20:24:17 -0500 Message-ID: <20051122202417.3xeq2oaicm2o4oso@webmail.mit.edu> Date: Tue, 22 Nov 2005 20:24:17 -0500 From: "Xiaoran (Sharon) Zhang" To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] Week 12 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: 982 Content-Length: 517 X-Keywords: NonJunk THe Monty Hall problem was most interesting because it demonstrated how common sense might be deceiving in calculating probability. The 4 step method is also demonstrated to be very useful. ************************************************** 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 dowgun@MIT.EDU Tue Nov 22 21:22:10 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAN2MA5o026655 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 21:22:10 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAN2M9BV005389 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 21:22:09 -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 jAN2M3j4001062 for <6042-probs@theory.lcs.MIT.EDU>; Tue, 22 Nov 2005 21:22:03 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-3.mit.edu (8.12.4) id jAN2M3AU031886; Tue, 22 Nov 2005 21:22:03 -0500 Received: from PLP-ONE-FORTY-THREE.MIT.EDU (PLP-ONE-FORTY-THREE.MIT.EDU [18.218.1.143]) (User authenticated as dowgun@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Tue, 22 Nov 2005 21:22:03 -0500 Message-ID: <20051122212203.rxvlztqlteaoo0sk@webmail.mit.edu> Date: Tue, 22 Nov 2005 21:22:03 -0500 From: Neil M Dowgun To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] ln 12 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 983 Content-Length: 748 X-Keywords: I think I understand everything here, but I do have one question - how could the OJ DNA be pairwise independent but not mutually independent? I assume that two markers would only be pairwise independent if they were on different chromosones, otherwise there would be some recombination frequency. Thus, all five markers would be on different chromosones - how could any combination of markers/lack of markers affect the appearance/lack of a marker on a different chromosone? The example with the coins seems to not be mutually independent because there is a pigeonhole problem - there are three coins and only two outcomes! But here there should be 46 chromosones, and only five are being used. Was this really an argument used in this trial? Neil From hsoumare@MIT.EDU Tue Nov 22 22:02:42 2005 Return-Path: Received: from grand-central-station.mit.edu (GRAND-CENTRAL-STATION.MIT.EDU [18.7.21.82]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAN32g5o010061 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 22:02:42 -0500 Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by grand-central-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAN32fA1023206 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 22:02:42 -0500 (EST) Received: from [18.241.7.23] (NEW-FIVE-THIRTY-FOUR.MIT.EDU [18.241.7.23]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAN32Tok002012 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 22:02:29 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: <9CF52F48-4496-4C7A-825B-B3AF949B96A7@mit.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Hamidou Soumare Subject: {Sayan} Weekly Email Comment Date: Tue, 22 Nov 2005 22:11:57 -0500 X-Mailer: Apple Mail (2.746.2) X-Spam-Score: 3.631 X-Spam-Level: *** (3.631) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 984 Content-Length: 120 X-Keywords: NonJunk Hi, Could you please go over where the Law of Total Probability on pg 17 comes from more in detail? Thanks. Hamidou From hkhall@MIT.EDU Tue Nov 22 22:13:38 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 jAN3Dc5o020682 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 22:13:38 -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 jAN3DaBV010502; Tue, 22 Nov 2005 22:13:36 -0500 (EST) Received: from [18.96.5.125] (SIMMONS-ONE-TWENTY-FIVE.MIT.EDU [18.96.5.125]) (authenticated bits=0) (User authenticated as hkhall@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN3DTBJ008773 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT); Tue, 22 Nov 2005 22:13:29 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v623) Message-Id: Content-Type: multipart/alternative; boundary=Apple-Mail-1--210413645 To: 6042-probs@theory.csail.mit.edu Subject: [David] Week 12 Comments From: Harrison King Hall Date: Tue, 22 Nov 2005 22:13:28 -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 X-UID: 985 Content-Length: 1711 X-Status: A X-Keywords: NonJunk --Apple-Mail-1--210413645 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=ISO-2022-JP; format=flowed David- Wow, I know nothing about probability. Well not absolutely nothing, but close enough for the rigor required by this course. By far the most interesting case in probability that I had not even considered was Posteriori probabilities. I had always heard and made phrases like that, but now I understand where the mathematical basis is from. I realize it is only a special case of conditional probability, but I think it is awesome. The most difficult thing for me for a long time was independence since I didn't find a rigorous definition of Pr{A $B"A(B B} in the notes. Maybe it was there but I didn't catch it for a while and I am still a little fuzzy on it. -Harrison --Apple-Mail-1--210413645 Content-Transfer-Encoding: 7bit Content-Type: text/enriched; charset=ISO-2022-JP David- Wow, I know nothing about probability. Well not absolutely nothing, but close enough for the rigor required by this course. By far the most interesting case in probability that I had not even considered was Posteriori probabilities. I had always heard and made phrases like that, but now I understand where the mathematical basis is from. I realize it is only a special case of conditional probability, but I think it is awesome. The most difficult thing for me for a long time was independence since I didn't find a rigorous definition of Pr{A Hiragino Kaku Gothic Pro$B"A(B B} in the notes. Maybe it was there but I didn't catch it for a while and I am still a little fuzzy on it. -Harrison --Apple-Mail-1--210413645-- From ozcan@MIT.EDU Tue Nov 22 22:26:20 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 jAN3QK5o002359 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 22:26:20 -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 jAN3QJA1024013 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 22:26:20 -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 jAN3QGMv012154 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 22:26:16 -0500 (EST) Message-Id: <5.2.1.1.2.20051122221658.020e5e50@po12.mit.edu> X-Sender: ozcan@hesiod (Unverified) X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Tue, 22 Nov 2005 22:26:12 -0500 To: 6042-probs@theory.lcs.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: 986 Content-Length: 209 X-Keywords: I found the conditional probability equation very interesting and helpful. It is at the start of Section 3. Prob(A intersection B ) = Prob (A given B) / Prob (B) = Prob (B given A) / Prob (A) Yasin Ozcan From aston@MIT.EDU Tue Nov 22 22:29:41 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 jAN3Te5o003663 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 22:29:40 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAN3TdBV021921 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 22:29:39 -0500 (EST) Received: from astonlaptop (NEW-SEVENTY-TWO.MIT.EDU [18.241.5.72]) (authenticated bits=0) (User authenticated as aston@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN3Ta3Q011463 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 22:29:37 -0500 (EST) Message-Id: <200511230329.jAN3Ta3Q011463@outgoing.mit.edu> Reply-To: From: "Aston Motes" To: <6042-probs@theory.csail.mit.edu> Subject: [Hanson] Week 12 Comments Date: Tue, 22 Nov 2005 22:29:34 -0500 Organization: MIT MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_008F_01C5EFB4.371BFCE0" X-Mailer: Microsoft Office Outlook, Build 11.0.6353 Thread-Index: AcXv3h9LzzwOav+fR5amhjEmiRaPIQ== X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: 0.313 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 987 Content-Length: 1644 X-Keywords: This is a multi-part message in MIME format. ------=_NextPart_000_008F_01C5EFB4.371BFCE0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit The notes claim that two events are independent iff the probabilities multiply to their intersection with no proof of the statement (page 22). I'm pretty sure I lost points on a 6.041 test for using this proposition and have, ever since, been sort of wary of using that reasoning to prove independence. Is it provable or is it a definition for this course? - Aston ------=_NextPart_000_008F_01C5EFB4.371BFCE0 Content-Type: text/html; charset="us-ascii" Content-Transfer-Encoding: quoted-printable
The = notes claim that=20 two events are independent iff the probabilities multiply to their = intersection=20 with no proof of the statement (page 22). I'm pretty sure I lost points = on a=20 6.041 test for using this proposition and have, ever since, been sort of = wary of=20 using that reasoning to prove independence. Is it provable or is it a = definition=20 for this course?
 
    -=20 Aston
------=_NextPart_000_008F_01C5EFB4.371BFCE0-- From meyer@imap.theory.csail.mit.edu Tue Nov 22 20:13:59 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 jAN1Dx5o018225 for <6042-webmaster@theory.csail.mit.edu>; Tue, 22 Nov 2005 20:13:59 -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 jAN1Dv26026535 for <6042-webmaster@theory.csail.mit.edu>; Tue, 22 Nov 2005 20:13:58 -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 jAN1Dv4N021229 for <6042-webmaster@theory.csail.mit.edu>; Tue, 22 Nov 2005 20:13:57 -0500 (EST) Received: from [18.246.1.160] (TYLERW.MIT.EDU [18.246.1.160]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAN1DtMu006043 for <6042-webmaster@theory.csail.mit.edu>; Tue, 22 Nov 2005 20:13:55 -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-webmaster@theory.csail.mit.edu From: Tyler Williams Subject: (Sayan) email comment Date: Tue, 22 Nov 2005 20:13:45 -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 Content-Length: 181 X-UID: 988 X-Keywords: NonJunk It would be cool if, in class, we could go over a little bit more of drawing the probability trees. Also, I thought the game show thing was cool because it was so unintuitive. From meyer@imap.theory.csail.mit.edu Tue Nov 22 20:58:17 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 jAN1wG5o004887 for <6042-staff@theory.csail.MIT.EDU>; Tue, 22 Nov 2005 20:58:17 -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 jAN1wF26000739 for <6042-staff@theory.csail.MIT.EDU>; Tue, 22 Nov 2005 20:58:16 -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 jAN1wF4N022729; Tue, 22 Nov 2005 20:58:15 -0500 (EST) Received: from [192.168.1.104] (c-66-30-24-123.hsd1.ma.comcast.net [66.30.24.123]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAN1w7Mu007837; Tue, 22 Nov 2005 20:58:07 -0500 (EST) Message-ID: <4383CCAE.5030709@theory.lcs.mit.edu> Date: Tue, 22 Nov 2005 20:58:06 -0500 From: sayan mitra User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Jesus Medrano , 6042-staff@theory.csail.MIT.EDU Subject: Re: [Sayan] indepence with conditional reading assignment References: <1132690759.17310.1.camel@localhost> In-Reply-To: <1132690759.17310.1.camel@localhost> 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 Content-Length: 419 X-UID: 989 X-Keywords: NonJunk Jesus Medrano wrote: >What is suppose to be done when the events in conditional probability >are independent. > Well, if A and B are independent, then as shown in the notes, P(A|B) = P(A /\ B) / P(B) = P(A). > Also what is suppose to be done when the conditional >probability has more than one dependent event. > > I don't quite understand this question, can you rephrase it ? Best, Sayan >Jesus Medrano > > From meyer@imap.theory.csail.mit.edu Tue Nov 22 16:39:54 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 jAMLdr5o009561 for ; Tue, 22 Nov 2005 16:39:53 -0500 Received: from smtp104.mail.sc5.yahoo.com ([66.163.169.223]) by rozz.csail.mit.edu with smtp (Exim 4.50) id 1Eefrl-0004S5-85 for meyer@csail.mit.edu; Tue, 22 Nov 2005 16:39:53 -0500 Received: (qmail 69679 invoked from network); 22 Nov 2005 21:39:52 -0000 Received: from unknown (HELO ?192.168.1.103?) (armeyer10@71.248.165.112 with plain) by smtp104.mail.sc5.yahoo.com with SMTP; 22 Nov 2005 21:39:52 -0000 Mime-Version: 1.0 (Apple Message framework v623) Content-Type: text/plain; charset=US-ASCII; format=flowed Message-Id: <48e5d16a79172eeeef6f1335b36137bd@csail.mit.edu> Content-Transfer-Encoding: 7bit From: "Albert R. Meyer" Subject: Fwd: [Hanson] Reading Comments 12 (fwd) Date: Tue, 22 Nov 2005 16:39:51 -0500 To: dnreshef@MIT.EDU X-Mailer: Apple Mail (2.623) X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on theory.csail.mit.edu X-Spam-Level: X-Spam-Status: No, hits=-4.9 required=3.7 tests=AWL,BAYES_00 autolearn=ham version=2.63 Status: RO Content-Length: 1502 X-UID: 990 X-Keywords: Begin forwarded message: > From: "Albert R. Meyer" > Date: November 22, 2005 4:37:56 PM EST > To: Hanson M Zhou > Subject: Re: [Hanson] Reading Comments 12 (fwd) > > email ink should work now... > regards, A. > On Nov 22, 2005, at 3:24 PM, Hanson M Zhou wrote: > >> One more... >> >> ---------- Forwarded message ---------- >> Date: Tue, 22 Nov 2005 15:18:59 -0500 >> From: David N Reshef >> To: hmzhou@mit.edu >> Subject: Fwd: [Hanson] Reading Comments 12 >> >> Hanson, >> I've tried emailing my comments twice now to >> 6042-probs@theory.lcs.MIT.EDU, >> and both times, it said that it was an inccorrect adress. If that is >> an >> incorrect adress, could you please send me the real one. In any >> case, my >> reading comments for tomorrow are forwarded below. >> -Dave >> >> >> >> ----- Forwarded message from dnreshef@MIT.EDU ----- >> Date: Tue, 22 Nov 2005 13:11:49 -0500 >> From: David N Reshef >> Reply-To: David N Reshef >> Subject: [Hanson] Reading Comments 12 >> To: 6042-probs@theory.lcs.MIT.EDU >> >> This week's reading was particularly easy, and I think I understood >> just about >> everything. I did, however, find the sections on infinite sample >> spaces (like >> yesterday's in class problem) and conditional probability (we have >> done a lot >> with this in my genetics class) particularly interesting. >> -Dave >> >> >> ----- End forwarded message ----- From fluff@MIT.EDU Tue Nov 22 23:07:43 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 jAN47h5o017652 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 23:07:43 -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 jAN47gMV015530 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 23:07:42 -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 jAN47es4017228 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 23:07:40 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v734) Content-Transfer-Encoding: 7bit Message-Id: <24438ECC-3BFD-4D89-A4C6-57C3D7560165@MIT.EDU> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Crystal Chao Subject: [Jelani] week 12 reading Date: Tue, 22 Nov 2005 23:05:58 -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: 991 Content-Length: 152 X-Keywords: NonJunk I thought the reading very effectively conveyed the fact that probability is a completely unintuitive subject. It was really depressing. ~Crystal From benlu@MIT.EDU Tue Nov 22 23:31:15 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 jAN4VF5o028090 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 23:31:15 -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 jAN4VEMV000960 for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 23:31:14 -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 jAN4UwUc020393 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Tue, 22 Nov 2005 23:30:58 -0500 (EST) Message-ID: <4383F089.5000002@mit.edu> Date: Tue, 22 Nov 2005 23:31:05 -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 12 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: 992 Content-Length: 425 X-Status: A X-Keywords: No real comments besides counter-intuitive things are cool, and I think I found two errors in the notes: * The first is the lower branch of the tree in the fair VS trick coin tree (top of page 19). I think it should read 1^100 and not (1/2)^100. * The second is the inclusion-exclusion formula (page 22) "Pr{A|BuC} = Pr{A|C} + Pr{A|C} - Pr{AnB|C}" which should read "Pr{A|BuC} = Pr{A|C} + Pr{B|C} - Pr{AnB|C}" ~Ben Lu From tonyng@MIT.EDU Tue Nov 22 23:36:33 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 jAN4aX5o028417 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 23:36:33 -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 jAN4aWMV004251 for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 23:36:32 -0500 (EST) Received: from TNG.mit.edu (BURTON-SIX-EIGHTY-NINE.MIT.EDU [18.247.7.178]) (authenticated bits=0) (User authenticated as tonyng@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN4aFU2021088 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 22 Nov 2005 23:36:16 -0500 (EST) Message-Id: <5.2.1.1.2.20051122232734.00bb1688@po9.mit.edu> X-Sender: tonyng@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Tue, 22 Nov 2005 23:36:30 -0500 To: 6042-probs@theory.csail.mit.edu From: Tony Ng Subject: [Jelani] Reading Comments Week 12 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: 993 Content-Length: 389 X-Keywords: I found the "Medical Testing" example (Section 3.6 on pg20) very interesting. It made me more aware about how easy it is to just listen to some numbers and be fooled by what it actually means. I think it is a great example to show that it is important to calculate probabilities carefully because initially intuition led me to think that this medical test wasn't too bad. - Tony Ng From sergiob@MIT.EDU Wed Nov 23 00:14:59 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 jAN5Ex5o003595 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 00:14:59 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAN5EwMV027269 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 00:14:58 -0500 (EST) Received: from mit-kf7uwcnbdr4.mit.edu (SENIOR-THREE-FIFTY-EIGHT.MIT.EDU [18.244.6.103]) (authenticated bits=0) (User authenticated as sergiob@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN5Eq8r026041 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 00:14:53 -0500 (EST) Message-Id: <5.2.1.1.2.20051122220644.00c3e5e8@po14.mit.edu> X-Sender: sergiob@po14.mit.edu X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Tue, 22 Nov 2005 22:14:51 -0700 To: 6042-probs@theory.csail.mit.edu From: Sergio Bacallado Subject: [David] Week 12 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 994 Content-Length: 316 X-Keywords: I found the topic of independence very interesting. I wonder if there is a simpler way to determine independence between events, because evaluating the probabilities of intersections for every possible subset of outcomes must become cumbersome as the outcome space becomes very large. Sergio Bacallado Group A. From yaser@MIT.EDU Wed Nov 23 00:24:31 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 jAN5OV5o004267 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 00:24:31 -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 jAN5OUMV002656 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 00:24:30 -0500 (EST) Received: from Charizard (NEW-THREE-SEVENTY-FOUR.MIT.EDU [18.241.6.119]) (authenticated bits=0) (User authenticated as ykhan@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN5OJF6027049 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 00:24:28 -0500 (EST) Message-Id: <200511230524.jAN5OJF6027049@outgoing.mit.edu> From: "Yaser Khan" To: <6042-probs@theory.lcs.mit.edu> Subject: David- tp12 reading comments Date: Wed, 23 Nov 2005 00:24:12 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_00BB_01C5EFC4.41F8CCA0" X-Mailer: Microsoft Office Outlook, Build 11.0.6353 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcXv7iM3r6FldEKuT/ahzJnaWuCXjA== X-Spam-Score: 5.851 X-Spam-Level: ***** (5.851) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 995 Content-Length: 5675 X-Keywords: NonJunk This is a multi-part message in MIME format. ------=_NextPart_000_00BB_01C5EFC4.41F8CCA0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit Hi David, At first read, the prob stuff seemed pretty similar to that in 6.041, with just a few more rigorous definitions. I was wondering, what are some of the other caveats/subtleties with the pairwise/mutually independent definition? (The one given is that it's possibly for three events to not be mutually independent, even though their pairs are.) Thanks! _Yaser ------=_NextPart_000_00BB_01C5EFC4.41F8CCA0 Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: quoted-printable

Hi = David,

 

At first read, the prob stuff seemed pretty similar to that in 6.041, with just a few more = rigorous definitions. I was wondering, what are some of the other = caveats/subtleties with the pairwise/mutually independent = definition?  (The one given is that = it’s possibly for three events to not be mutually independent, even though their pairs = are.)

 

Thanks!

 

_Yaser =

------=_NextPart_000_00BB_01C5EFC4.41F8CCA0-- From a_lopez@MIT.EDU Wed Nov 23 01:16:16 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 jAN6GG5o020805 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 01:16:16 -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 jAN6GEMV002363 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 01:16:15 -0500 (EST) Received: from [18.234.1.61] (DP-SIXTY-ONE.MIT.EDU [18.234.1.61]) (authenticated bits=0) (User authenticated as a_lopez@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN6GCGo002238 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 01:16:13 -0500 (EST) Message-ID: <43840932.3040503@mit.edu> Date: Wed, 23 Nov 2005 01:16:18 -0500 From: Adriana Lopez User-Agent: Mozilla Thunderbird 1.0 (Windows/20041206) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.csail.mit.edu Subject: [Jelani] week 12 readings Content-Type: multipart/mixed; boundary="------------030201030901050307070104" X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 996 Content-Length: 1145 X-Keywords: NonJunk This is a multi-part message in MIME format. --------------030201030901050307070104 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit --------------030201030901050307070104 Content-Type: message/rfc822; name="[Jelani] week 12 readings" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="[Jelani] week 12 readings" Message-ID: <4382933A.1080904@mit.edu> Date: Mon, 21 Nov 2005 22:40:42 -0500 From: Adriana Lopez User-Agent: Mozilla Thunderbird 1.0 (Windows/20041206) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.csail.mit.edu Subject: [Jelani] week 12 readings Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit I didn't really understand section 3.7 ("other identities"). How is the formula Pr{A U B | C} = Pr{A | C} + Pr{A | C} - Pr{A n B | C} derived? Why not write it Pr{A U B | C} = 2Pr{A | C} - Pr{A n B | C}. Why is the other formula not valid? And why is B n C empty? I also thought the DNA example was specially confusing. Adriana --------------030201030901050307070104-- From mracich@MIT.EDU Wed Nov 23 01:20:38 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 jAN6Kc5o021089 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 01:20:38 -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 jAN6Kctd029422 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 01:20:38 -0500 (EST) Received: from MACGREGOR-THREE-FORTY-FIVE.MIT.EDU (MACGREGOR-THREE-FORTY-FIVE.MIT.EDU [18.239.6.90]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAN6KZMu019508 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 01:20:35 -0500 (EST) Subject: [Sayan] Comments for Course Notes, Week 12 (Introduction to Probability) From: Moira Racich To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Wed, 23 Nov 2005 01:20:34 -0500 Message-Id: <1132726835.8136.6.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.4.1 Content-Transfer-Encoding: 7bit X-Spam-Score: 2.706 X-Spam-Level: ** (2.706) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 997 Content-Length: 235 X-Keywords: I found section 5. "Mutual Independence", (starting on page 24) confusing. I would appreciate it if this was explained further. Also, in general, I am confused about how to convert from set notation to probabilities. Moira Racich From brevzin@MIT.EDU Wed Nov 23 01:21:53 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 jAN6Lr5o021213 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 01:21:53 -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 jAN6LqMV005371 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 01:21:52 -0500 (EST) Received: from BARRY.mit.edu (PLP-ONE-TWENTY-FOUR.MIT.EDU [18.218.1.124]) (authenticated bits=0) (User authenticated as brevzin@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN6LjYL002768 (version=TLSv1/SSLv3 cipher=DES-CBC3-SHA bits=168 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 01:21:45 -0500 (EST) Message-Id: <6.1.2.0.1.20051123012009.019fe210@po14.mit.edu> X-Sender: brevzin@hesiod X-Mailer: QUALCOMM Windows Eudora Version 6.1.2.0 Date: Wed, 23 Nov 2005 01:21:50 -0500 To: 6042-probs@theory.csail.mit.edu From: Barry Revzin Subject: [Hanson] Reading Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 998 Content-Length: 204 X-Keywords: Um, yeah, I'm learning all this stuff in 18.103 (Measure Theory). Um. Yeah. Union bound is called subadditivity, I thing it makes more sense conceptually. Otherwise... Have a good thanksgiving? Barry From kktyan@MIT.EDU Wed Nov 23 01:45:11 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 jAN6jB5o002222 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 01:45:11 -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 jAN6jAMV017269 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 01:45:10 -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 jAN6j45K004515 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 01:45:04 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-6.mit.edu (8.12.4) id jAN6j3qg015626; Wed, 23 Nov 2005 01:45:03 -0500 Received: from BURTON-THREE-THIRTY-SIX.MIT.EDU (BURTON-THREE-THIRTY-SIX.MIT.EDU [18.247.6.81]) (User authenticated as kktyan@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 23 Nov 2005 01:45:03 -0500 Message-ID: <20051123014503.5lactfb6xr4kowcs@webmail.mit.edu> Date: Wed, 23 Nov 2005 01:45:03 -0500 From: Karena Tyan To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] Reading Comments 12 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 999 Content-Length: 764 X-Keywords: Just for clarification (this isn't my main question), two events that are independent are *also* mutually independent, by the definition of independence and mutual independence, correct? (pages 23-25) I am confused about the a posteriori probability covered in pages 17-18. In the tutor problem 12.2, it is said that Pr{A} = 0.8 and Pr{L} = 0.4; in a case like this, how would you compute Pr{L|A} without being given that it is 0.3? I mean, I know that Pr{L|A} = Pr{A n L}/Pr{L}, but A n L is dependent upon the value of Pr{A|L}, which is in turn dependent upon the value of Pr{L|A} in that Pr{A|L} = Pr{A n L}/Pr{L}. In general, I'm just a little confused over how to find A n B or Pr{A|B}. - Karena -- 410 Memorial Drive Cambridge, MA 02139 (585)957-5923 From dnreshef@MIT.EDU Wed Nov 23 02:25:43 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 jAN7Ph5o029046 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 02:25:43 -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 jAN7PgLX003989 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 02:25:42 -0500 (EST) Received: from w92-130-webmail-1.mit.edu (W92-130-WEBMAIL-1.MIT.EDU [18.7.22.131]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN7PZlq006925 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 02:25:35 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-1.mit.edu (8.12.4) id jAN7PYC5019523; Wed, 23 Nov 2005 02:25:34 -0500 Received: from pcp09558804pcs.verona01.nj.comcast.net (pcp09558804pcs.verona01.nj.comcast.net [68.36.248.152]) (User authenticated as dnreshef@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 23 Nov 2005 02:25:34 -0500 Message-ID: <20051123022534.pcraj4vpmx440c4g@webmail.mit.edu> Date: Wed, 23 Nov 2005 02:25:34 -0500 From: David N Reshef To: 6042-probs@theory.lcs.MIT.EDU Subject: [Hanson] Reading Comments 12 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1000 Content-Length: 300 X-Keywords: This week's reading was particularly easy, and I think I understood just about everything. I did, however, find the sections on infinite sample spaces (like yesterday's in class problem) and conditional probability (we have done a lot with this in my genetics class) particularly interesting. -Dave From mdmurray@MIT.EDU Wed Nov 23 02:37:56 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 jAN7bu5o001810 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 02:37:56 -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 jAN7bu0h001639 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 02:37:56 -0500 (EST) Received: from [18.234.0.116] (MDMURRAY.MIT.EDU [18.234.0.116]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAN7bhok013295 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 02:37:44 -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.csail.mit.edu From: Michael Murray Subject: [Hanson] ln12 reading Date: Wed, 23 Nov 2005 02:36:28 -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: 1001 Content-Length: 445 X-Status: A X-Keywords: NonJunk I found it surprising that the independence equation was Pr(A n B) = Pr(A).Pr(B). My original thought was that the A and B would be independent if Pr(A u B) = Pr(A) + Pr(B), this would imply that there is no overlap in the sets A and B and so they would be independent. I am not sure where this intuition fails and why we instead look at the intersection. What is the intuition behind multiplying two probabilities? Michael Murray From bilodeau@MIT.EDU Wed Nov 23 02:52:09 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAN7q95o013295 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 02:52:09 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAN7q8LX015134 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 02:52:08 -0500 (EST) Received: from pbilodeau (MACGREGOR-TWO-TWENTY-ONE.MIT.EDU [18.239.5.221]) (authenticated bits=0) (User authenticated as bilodeau@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN7q1Qv008371 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 02:52:02 -0500 (EST) Message-Id: <200511230752.jAN7q1Qv008371@outgoing.mit.edu> From: "Peter Bilodeau" To: <6042-probs@theory.lcs.mit.edu> Subject: [jelani] reading comments Date: Wed, 23 Nov 2005 02:51:48 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0000_01C5EFD8.D992D420" X-Mailer: Microsoft Office Outlook, Build 11.0.5510 Thread-Index: AcXwAsHw61iyGuDqR7+6BKtt20MGhw== X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: 2.779 X-Spam-Level: ** (2.779) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1002 Content-Length: 2255 X-Keywords: NonJunk This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C5EFD8.D992D420 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit This reading was, I think, made unduly confusing, especially in the "four step method" section. The method was explained by means of an example, but an overall summary of the process is hard to extract from amidst the rest of the explanation. Peter Bilodeau ------=_NextPart_000_0000_01C5EFD8.D992D420 Content-Type: text/html; charset="us-ascii" Content-Transfer-Encoding: quoted-printable

This reading was, I think, made unduly confusing, = especially in the “four step method” section.  The method was = explained by means of an example, but an overall summary of the process is hard to = extract from amidst the rest of the explanation.

 

Peter Bilodeau

------=_NextPart_000_0000_01C5EFD8.D992D420-- From ksindi@MIT.EDU Wed Nov 23 02:55:25 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAN7tP5o020751 for <6042-probs@theory.csail.MIT.EDU>; Wed, 23 Nov 2005 02:55:25 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAN7tNLX016540 for <6042-probs@theory.csail.MIT.EDU>; Wed, 23 Nov 2005 02:55:24 -0500 (EST) Received: from w92-130-webmail-1.mit.edu (W92-130-WEBMAIL-1.MIT.EDU [18.7.22.131]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN7tF9k008561 for <6042-probs@theory.csail.MIT.EDU>; Wed, 23 Nov 2005 02:55:16 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-1.mit.edu (8.12.4) id jAN7tFYH021237; Wed, 23 Nov 2005 02:55:15 -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 ; Wed, 23 Nov 2005 02:55:15 -0500 Message-ID: <20051123025515.8qd9e0hgiie8oso4@webmail.mit.edu> Date: Wed, 23 Nov 2005 02:55:15 -0500 From: Kamil Y Sindi To: 6042-probs@theory.csail.MIT.EDU Subject: [David] Week 12 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: 1003 Content-Length: 170 X-Keywords: I found the many detailed examples very helpful. To me, the touphest part is getting around in modeling conditional probability in to a formula as I always get mixed up. From lmccart@MIT.EDU Wed Nov 23 03:48:08 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 jAN8m85o007607 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 03:48:08 -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 jAN8m6LX008498 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 03:48:07 -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 jAN8m2sT011102 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 03:48:02 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jAN8m2qK025958; Wed, 23 Nov 2005 03:48:02 -0500 Received: from AP-FIFTY-ONE.MIT.EDU (AP-FIFTY-ONE.MIT.EDU [18.153.1.51]) (User authenticated as lmccart@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 23 Nov 2005 03:48:02 -0500 Message-ID: <20051123034802.pu7i84sxi1hicoo4@webmail.mit.edu> Date: Wed, 23 Nov 2005 03:48:02 -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: 1004 Content-Length: 141 X-Keywords: I understood the reading but a review of the section about posteriori probabilities like on the tutor problems would be appreciated. -lauren From shreyes19@gmail.com Wed Nov 23 03:48:47 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 jAN8mk5o009512 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 03:48:46 -0500 Received: from nproxy.gmail.com ([64.233.182.192]) by rozz.csail.mit.edu with esmtp (Exim 4.50) id 1EeqJ4-0006Pa-G8 for 6042-probs@theory.lcs.mit.edu; Wed, 23 Nov 2005 03:48:46 -0500 Received: by nproxy.gmail.com with SMTP id l36so227711nfa for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 00:47:45 -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=SYz8Bcsn2N2wkCxsBMZPzTybtBky1W+ZO1U6DyBxK2VivssTchCoBUiRBXryPyf4TpWTceBcf0K1ZiYftQcJlzwNDZysniLwxDxiMOmMI/BnQIPhnH3Kdi1DNpMRwIirEwA4RsKkpxzLxxg+kYE4aBnG0th7kHSP1VrrxeXV6AA= Received: by 10.48.225.2 with SMTP id x2mr1760nfg; Tue, 22 Nov 2005 23:44:18 -0800 (PST) Received: by 10.48.161.8 with HTTP; Tue, 22 Nov 2005 23:44:18 -0800 (PST) Message-ID: <3c33fe380511222344j1453ec0em8813e669c3946e51@mail.gmail.com> Date: Wed, 23 Nov 2005 02:44:18 -0500 From: Shreyes Seshasai Sender: shreyes19@gmail.com To: 6042-probs@theory.lcs.mit.edu Subject: [Sayan] Week 12 Reading Comments MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_2798_21161657.1132731858295" Status: RO X-UID: 1005 Content-Length: 1623 X-Keywords: NonJunk ------=_Part_2798_21161657.1132731858295 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Hi, The part of the notes that most interested me was section 3.6 - Medical Testing (pg 20-21). I was able to follow the derivation of the conditional probability of 1/4 that you have the disease if tested positively. I think it would be good to see more examples in class of cases where drawing out the probability tree and calculating leads to non-intuitive answers, especially when working with conditional probabilities. These tend to be the more interesting ones, at least compared with regular probabilities wit= h discrete random variables (like questions with coin flips). Thanks, Shreyes Group 7 ------=_Part_2798_21161657.1132731858295 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Content-Disposition: inline Hi,

The part of the notes that most interested me was section 3.6 - Medical Testing (pg 20-21).  I was able to follow the derivation of the conditional probability of 1/4 that you have the disease if tested positively.  I think it would be good to see more examples in class of cases where drawing out the probability tree and calculating leads to non-intuitive answers, especially when working with conditional probabilities.  These tend to be the more interesting ones, at least compared with regular probabilities with discrete random variables (like questions with coin flips).

Thanks,
Shreyes
Group 7
------=_Part_2798_21161657.1132731858295-- From ctsims@MIT.EDU Wed Nov 23 03:56:48 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 jAN8um5o011980 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 03:56:48 -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 jAN8ulLX011889 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 03:56:47 -0500 (EST) Received: from HowardRoark.mit.edu (EASTCAMPUS-NINE-TWENTY-TWO.MIT.EDU [18.238.6.155]) (authenticated bits=0) (User authenticated as ctsims@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN8ueOb011489 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 03:56:40 -0500 (EST) Message-Id: <5.2.1.1.2.20051123035151.10020518@po12.mit.edu> X-Sender: ctsims@po12.mit.edu X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 23 Nov 2005 03:54:39 -0500 To: 6042-probs@theory.lcs.mit.edu From: Clayton Sims Subject: [6.042] Reading problem - Clayton Sims Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1006 Content-Length: 284 X-Keywords: NonJunk I think that the passage and formula on pg. 13 about conditional probability could require most explanation. Primarily the introduction and use of the A (intersection) B probability, and how it is derived. I think this would be a good thing to talk about in class. -Clayton Sims From mpapi@MIT.EDU Wed Nov 23 04:36:20 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAN9aK5o027159 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 04:36:20 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAN9aJLX027280 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 04:36:19 -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 jAN9aDFo013027 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 04:36:13 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-4.mit.edu (8.12.4) id jAN9aDpk029142; Wed, 23 Nov 2005 04:36:13 -0500 Received: from MACGREGOR-THREE-FORTY-FIVE.MIT.EDU (MACGREGOR-THREE-FORTY-FIVE.MIT.EDU [18.239.6.90]) (User authenticated as mpapi@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 23 Nov 2005 04:36:13 -0500 Message-ID: <20051123043613.vuyh0wis0jykockk@webmail.mit.edu> Date: Wed, 23 Nov 2005 04:36:13 -0500 From: Matthew M Papi To: 6042-probs@theory.lcs.MIT.EDU Subject: [Jelani] week 12 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: 1007 Content-Length: 145 X-Keywords: NonJunk Section 5 on Mutual Independence, pages 24ff. This stuff was tricky the first time around in 6.041, so the more explanation the better. - Matt From kevin08@MIT.EDU Wed Nov 23 05:05:18 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 jANA5I5o003197 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 05:05:18 -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 jANA5GKh007810 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 05:05:16 -0500 (EST) Received: from kevlar.mit.edu (NEXT-THREE-FIFTY-SEVEN.MIT.EDU [18.242.6.102]) (authenticated bits=0) (User authenticated as kevin08@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAN9vqUB013841 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 04:57:53 -0500 (EST) Message-Id: <6.2.3.4.2.20051123044514.02a12490@po10.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Wed, 23 Nov 2005 04:57:39 -0500 To: 6042-probs@theory.lcs.mit.edu From: Kevin Wang Subject: [Hanson] Reading Comments Mime-Version: 1.0 Content-Type: multipart/mixed; boundary="=====================_68461522==_" X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1008 Content-Length: 481920 X-Keywords: --=====================_68461522==_ Content-Type: text/plain; charset="us-ascii"; format=flowed Hi, I have no questions about this week's reading since I'm taking 6.041 at the same time and we covered this material already. However, I think it might be helpful to students if you explain Total Probability Theorem (Section 3.3) to them with a diagram like the one I attached. I found that picture very helpful when learning it. Kevin --=====================_68461522==_ Content-Type: application/octet-stream; name="total probability theorem.bmp" Content-Transfer-Encoding: base64 Content-Disposition: attachment; filename="total probability theorem.bmp" Qk2CbwUAAAAAADYAAAAoAAAADAEAALsBAAABABgAAAAAAExvBQAAAAAAAAAAAAAAAAAAAAAA//// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////AAAA AAAAAAAA//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////4eHhAAAAAAAAjIyM//////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////jIyMAAAAAAAA4eHh//////////////////////////// ////////////////////////////////////////////////////////////4eHhAAAAAAAAjIyM //////////////////////////////////////////////////////////////////////////// ////AAAAAAAAAAAA//////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////jIyM AAAAAAAA4eHh//////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////jIyMAAAAAAAA4eHh//////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////4eHhAAAAAAAAjIyM//////////////////// ////////////////////////////////////////////////////////////////////jIyMAAAA AAAA4eHh//////////////////////////////////////////////////////////////////// ////////////AAAAAAAAAAAA//////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////4eHhAAAAAAAAjIyM//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////6enpAAAAAAAAfHx8//////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////jIyMAAAAAAAA6enp//////// ////////////////////////////////////////////////////////////////////////6enp AAAAAAAAfHx8//////////////////////////////////////////////////////////////// ////////////////////AAAAAAAAAAAA//////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////jIyMAAAAAAAA6enp//////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////p6enAAAAAAAA0NDQ //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////0NDQAAAAAAAAp6en //////////////////////////////////////////////////////////////////////////// ////p6enAAAAAAAA0NDQ//////////////////////////////////////////////////////// ////////////////////////////AAAAAAAAAAAA//////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////0NDQAAAAAAAAp6en//////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////TU1NAAAA AAAA//////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////AAAA AAAATU1N//////////////////////////////////////////////////////////////////// ////////////TU1NAAAAAAAA//////////////////////////////////////////////////// ////////////////////////////////////AAAAAAAAAAAA//////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////AAAAAAAATU1N//////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////AAAAAAAAAAAA////////////////////////////////////////////////4eHh AAAAAAAAjIyM////////////fHx8AAAAAAAA0NDQ//////////////////////////////////// 0NDQAAAAAAAAfHx8////////////8PDwp6enTU1NAAAATU1Np6en8PDw//////////////////// ////jIyMAAAAAAAA4eHh////////////AAAAAAAAAAAA//////////////////////////////// ////////////////4eHhAAAAAAAAjIyM////////////////////AAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAjIyM0NDQ////////////////////AAAAAAAAAAAA////////fHx8AAAAAAAA 0NDQ////////////////////////////////////0NDQAAAAAAAAfHx8////////////8PDwp6en TU1NAAAATU1Np6en8PDw////////////////////////jIyMAAAAAAAA4eHh//////////////// 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--=====================_68461522==_-- From ryoung@MIT.EDU Wed Nov 23 07:44:41 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 jANCif5o026557 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 07:44:41 -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 jANCieKh013580 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 07:44:40 -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 jANCibsV022642 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 07:44:38 -0500 (EST) Message-Id: <6.2.3.4.2.20051123073853.02901450@po10.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.3.4 Date: Wed, 23 Nov 2005 07:44:39 -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: 1009 Content-Length: 545 X-Keywords: NonJunk I found the part about mutual independence tricky, although it seems relatively simple, I found myself getting it wrong on the Tutorial Problems as well as in the notes. Also, I have never heard of a posteriori problems before, but am getting used to them. I discovered that my last email comments never sent, so I will append them here. This entire notion is very new to me, so I feel behind already. It is difficult for me to look at a sequence and instantly find the generating functions, even on some of the trivial ones. -Ryan From mwangi@MIT.EDU Wed Nov 23 08:28:26 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 jANDSP5o014595 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 08:28:25 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jANDSOLG006060; Wed, 23 Nov 2005 08:28:24 -0500 (EST) Received: from IBM-1E80C73FC15.mit.edu (NEW-THREE-NINETY-NINE.MIT.EDU [18.241.6.144]) (authenticated bits=0) (User authenticated as mwangi@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANDSDPD029046 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT); Wed, 23 Nov 2005 08:28:17 -0500 (EST) Message-Id: <6.2.1.2.2.20051123082057.03a06eb0@po12.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.1.2 Date: Wed, 23 Nov 2005 08:28:11 -0500 To: 6042-probs@theory.lcs.mit.edu From: Timothy Mwangi Subject: [Sayan] Week 12 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: 1010 Content-Length: 258 X-Keywords: Passage: 3.4 A Posteriori Probabilities Page: 17 I found this passage most surprising because of the notion that we could use probability to say not only what will happen in the future but what happened in the past. Sincerely, Timothy M. Mwangi From nancyk@MIT.EDU Wed Nov 23 09:32:04 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 jANEW45o004569 for <6042-probs@theory.csail.MIT.EDU>; Wed, 23 Nov 2005 09:32:04 -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 jANEW2LG025301; Wed, 23 Nov 2005 09:32:02 -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 jANEVxpN015976; Wed, 23 Nov 2005 09:31:59 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-5.mit.edu (8.12.4) id jANEVxlD019946; Wed, 23 Nov 2005 09:31:59 -0500 Received: from WAREHOUSE-FOUR-NINETY-TWO.MIT.EDU (WAREHOUSE-FOUR-NINETY-TWO.MIT.EDU [18.139.6.237]) (User authenticated as nancyk@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 23 Nov 2005 09:31:59 -0500 Message-ID: <20051123093159.isipff4n878k8g48@webmail.mit.edu> Date: Wed, 23 Nov 2005 09:31:59 -0500 From: Nancy L Keuss To: 6042-probs@theory.csail.MIT.EDU Subject: [Hanson] Week 12 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: 1011 Content-Length: 306 X-Keywords: NonJunk Hi, I thought these notes were pretty straightforward and well-written, and I can't think of any difficulties to bring up. The applications of probability that the author brings up (tests for diseases, DNA testing) are interesting, and the way they are explained is very clear and logical. Thanks, Nancy From nedzel@MIT.EDU Wed Nov 23 09:39:47 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 jANEdl5o006073 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 09:39:47 -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 jANEdkLG002429 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 09:39:46 -0500 (EST) Received: from ThinkPadT43 (SIMMONS-ONE-NINETY-NINE.MIT.EDU [18.96.5.199]) (authenticated bits=0) (User authenticated as nedzel@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANEddut018520 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 09:39:40 -0500 (EST) Message-Id: <200511231439.jANEddut018520@outgoing.mit.edu> From: "David A. Nedzel" To: <6042-probs@theory.csail.mit.edu> Subject: [Sayan] Week 12 Comments Date: Wed, 23 Nov 2005 09:39:35 -0500 MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Mailer: Microsoft Office Outlook, Build 11.0.6353 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcW4zeo7ykLa/WaNRiGOpegAnm9CXA== X-Spam-Score: 2.777 X-Spam-Level: ** (2.777) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1012 Content-Length: 161 X-Keywords: NonJunk I've taken 6.041, so the notes this week seemed very straight-forward. Will we be covering much over the rest of the term that 6.041 doesn't touch on? - David From jehan@MIT.EDU Wed Nov 23 09:46:57 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 jANEkv5o007101 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 09:46:57 -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 jANEktLG008626 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 09:46:55 -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 jANEkruw021009 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 09:46:53 -0500 (EST) Message-Id: <5.2.1.1.2.20051123094356.00bc5c50@po14.mit.edu> X-Sender: jehan@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Wed, 23 Nov 2005 09:44:58 -0500 To: 6042-probs@theory.csail.mit.edu From: Jehan deFonseka Subject: [Sayan] Week 12 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1013 Content-Length: 91 X-Keywords: NonJunk This stuff is pretty easy. You should give the class the family boy/girl problem. jehan From arup@MIT.EDU Wed Nov 23 09:52:12 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jANEqB5o011425 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 09:52:12 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jANEqALG013433 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 09:52:10 -0500 (EST) Received: from [18.247.7.36] (BURTON-FIVE-FORTY-SEVEN.MIT.EDU [18.247.7.36]) (authenticated bits=0) (User authenticated as arup@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANEpsiV022711 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 09:51:54 -0500 (EST) Message-ID: <438481DC.9010407@mit.edu> Date: Wed, 23 Nov 2005 09:51:08 -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.lcs.mit.edu Subject: [Jelani] Week 12 Reading 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: 1014 Content-Length: 194 X-Keywords: Most of the probability reading seemed pretty straightforward, I guess the only thing is I was confused about independence (esp. mutual independence) section 5 p. 24 for a little bit. |Arup| From kromer@MIT.EDU Wed Nov 23 09:56:35 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 jANEuZ5o012000 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 09:56:35 -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 jANEuYLG017749 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 09:56:34 -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 jANEuWav024379 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 09:56:32 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-2.mit.edu (8.12.4) id jANEuWoQ012372; Wed, 23 Nov 2005 09:56:32 -0500 Received: from wibr-pub-7-101.wi.mit.edu (wibr-pub-7-101.wi.mit.edu [18.157.7.101]) (User authenticated as kromer@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 23 Nov 2005 09:56:32 -0500 Message-ID: <20051123095632.2gu2rfengjo84c8o@webmail.mit.edu> Date: Wed, 23 Nov 2005 09:56:32 -0500 From: Katherine A Romer To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] Email comments for reading MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1015 Content-Length: 260 X-Keywords: p. 24: "Here's a better mental picture of what independent events look like. The sample space is the whole rectangle. Event A is the vertical stripe, and event B is the horizontal stripe." I was confused by this diagram--what is it trying to show? Katherine From jstritar@MIT.EDU Wed Nov 23 10:12:50 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 jANFCo5o018040 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 10:12:50 -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 jANFCnLG005175 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 10:12:49 -0500 (EST) Received: from BAKER-FOUR-EIGHTY-NINE.MIT.EDU (BAKER-FOUR-EIGHTY-NINE.MIT.EDU [18.245.6.234]) (authenticated bits=0) (User authenticated as jstritar@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANFCfrT001093 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 10:12:42 -0500 (EST) Subject: [Sayan] Reading comments From: Jon Stritar To: 6042-probs@theory.lcs.mit.edu Content-Type: text/plain Date: Wed, 23 Nov 2005 10:12:40 -0500 Message-Id: <1132758760.19347.2.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: 1016 Content-Length: 294 X-Keywords: NonJunk 1.3 Step 1: Find the Sample Space I always think its amazing how important this step is for me to write down. Once I have the sample space down, and in the correct format for the problem, (like a tree, table, or all the events written out), the solution emerges quite naturally. Jon Stritar From vbrobbey@MIT.EDU Wed Nov 23 10:52:47 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 jANFqk5o008258 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 10:52:46 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jANFqjLG014734 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 10:52:45 -0500 (EST) Received: from napoleon (NAPOLEON-BONAPARTE.MIT.EDU [18.18.3.59]) (authenticated bits=0) (User authenticated as vbrobbey@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANFqbod016551 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 10:52:38 -0500 (EST) Message-ID: <001301c5f045$ed049f80$3b031212@napoleon> From: "Valery Kwasi Brobbey" To: <6042-probs@theory.csail.mit.edu> Subject: [Hanson] Week 12 Comments Date: Wed, 23 Nov 2005 10:52:35 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_0010_01C5F01C.032ABC10" 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: -0.718 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1017 Content-Length: 1335 X-Keywords: This is a multi-part message in MIME format. ------=_NextPart_000_0010_01C5F01C.032ABC10 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Probability is so far the topic I'm liking the most in the course. I = took some courses in high school that dealt probability but I've been = surprised by the analysis of the coin problem in the notes and the game = we looked at in class on Monday. It was cool to see applications f = probability in Medicin and Law. ------=_NextPart_000_0010_01C5F01C.032ABC10 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Probability is so far the topic I'm = liking the most=20 in the course. I took some courses in high school that dealt probability = but=20 I've been surprised by the analysis of the coin problem in the notes and = the=20 game we looked at in class on Monday. It was cool to see applications f=20 probability in Medicin and Law.
------=_NextPart_000_0010_01C5F01C.032ABC10-- From petek@MIT.EDU Wed Nov 23 10:53:13 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 jANFrD5o009123 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 10:53:13 -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 jANFrCLG015218 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 10:53:12 -0500 (EST) Received: from [128.30.5.10] (30-5-10.wireless.csail.mit.edu [128.30.5.10]) (authenticated bits=0) (User authenticated as petek@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANFr92B016770 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 10:53:10 -0500 (EST) Message-ID: <4384906B.2020106@mit.edu> Date: Wed, 23 Nov 2005 10:53:15 -0500 From: Pete Kruskall User-Agent: Mozilla Thunderbird 0.8 (Windows/20040913) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.lcs.mit.edu Subject: [Jelani] Probability Notes (This Week's Comments) Content-Type: multipart/alternative; boundary="------------040008090904050709070408" X-Spam-Score: 1.928 X-Spam-Level: * (1.928) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1018 Content-Length: 1550 X-Keywords: NonJunk This is a multi-part message in MIME format. --------------040008090904050709070408 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Probability is probably, as Ronnitt said, REALLY the most important thing we'll learn in this class. I'm looking forward to the conditional probability lecture today to help get a good picture of how to solve those kinds of problems. -P -- Pete Kruskall 28 The Fenway Boston, MA 02215 ::::::::::::::::::::::::::::: 617.536.9925 :::Sigma Nu::::: 508.843.5861 ::::Cell Phone:: ::::http://tege.mit.edu:::::: --------------040008090904050709070408 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Probability is probably, as Ronnitt said, REALLY the most important thing we'll learn in this class.  I'm looking forward to the conditional probability lecture today to help get a good picture of how to solve those kinds of problems.

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

:::::::::::::::::::::::::::::
617.536.9925 :::Sigma Nu:::::
508.843.5861 ::::Cell Phone::
::::http://tege.mit.edu::::::
--------------040008090904050709070408-- From meyer@imap.theory.csail.mit.edu Wed Nov 23 10:55:00 2005 Message-ID: <438490D4.4050201@csail.mit.edu> Date: Wed, 23 Nov 2005 10:55:00 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Benjamin Lu Subject: Re: [Jelani][6.042] comments on reading 12 References: <4383F089.5000002@mit.edu> In-Reply-To: <4383F089.5000002@mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 643 Status: RO X-UID: 1019 X-Keywords: Will fix 1/2^100. Thx for catching this. I think the text on p22 was correct, but I added a clarification (I hope it is anyway :-) in response to your concern. regards, A. Benjamin Lu wrote: > No real comments besides counter-intuitive things are cool, and I > think I found two errors in the notes: > * The first is the lower branch of the tree in the fair VS trick coin > tree (top of page 19). I think it should read 1^100 and not (1/2)^100. > * The second is the inclusion-exclusion formula (page 22) "Pr{A|BuC} = > Pr{A|C} + Pr{A|C} - Pr{AnB|C}" which should read "Pr{A|BuC} = Pr{A|C} > + Pr{B|C} - Pr{AnB|C}" > > ~Ben Lu > > From juang@MIT.EDU Wed Nov 23 10:58:13 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 jANFwD5o010901 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 10:58:13 -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 jANFvlLG020517 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 10:57:47 -0500 (EST) Received: from [18.238.5.154] (EASTCAMPUS-SIX-SIXTY-FIVE.MIT.EDU [18.238.5.154]) (authenticated bits=0) (User authenticated as juang@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANFvi7P018690 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 10:57:45 -0500 (EST) Message-ID: <4384916A.207@mit.edu> Date: Wed, 23 Nov 2005 10:57:30 -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.csail.mit.edu Subject: [David] Week 12 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: 1020 Content-Length: 268 X-Keywords: NonJunk I found it surprising (on page 27) that a set of pairwise independent events is not necessarily mutually independent. So much for intuition! I am actually working on that chessboard-tiling generating functions problem. ... Slowly. Have a good Thanksgiving, Jason. From zacharyozer@gmail.com Wed Nov 23 11:00:42 2005 Return-Path: Received: from wproxy.gmail.com (wproxy.gmail.com [64.233.184.193]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jANG0g5o011315 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 11:00:42 -0500 Received: by wproxy.gmail.com with SMTP id i30so870396wra for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 08:00:42 -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=PAXBZEC73KMl2iSnL3BQYAr3QbZ7g4jLa4IVxzxSHlvx473fWlez2eRd+RDmkdgoaFx93B8sb897N3nlbVcvfJAhXjdaDetiT/a7MYUZQ9EPmSzT1rZC583aVx5OweEszem9XEwSlszTVXHfKOUQPwygVXgja1t51Zbhd5JWcik= Received: by 10.65.103.12 with SMTP id f12mr6233395qbm; Wed, 23 Nov 2005 08:00:41 -0800 (PST) Received: by 10.65.152.13 with HTTP; Wed, 23 Nov 2005 08:00:41 -0800 (PST) Message-ID: <4f2613e50511230800t26b1610cm711c8049438076ca@mail.gmail.com> Date: Wed, 23 Nov 2005 11:00:41 -0500 From: Zachary Adam Ozer Sender: zacharyozer@gmail.com To: 6042-probs@theory.lcs.mit.edu Subject: Question regarding Posteriori Probabilities 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 jANG0g5o011315 Status: RO X-UID: 1021 Content-Length: 318 X-Keywords: NonJunk So, why is it that the probability of B given A is the interesction of A and B divided by the probability of A? This seems to give a circular definition if you substitute the intersection for the probability of A given B * probability of B and repeating for the probability of A given B. Best regards, Zachary Ozer From meyer@imap.theory.csail.mit.edu Wed Nov 23 11:04:45 2005 Message-ID: <4384931E.8060306@csail.mit.edu> Date: Wed, 23 Nov 2005 11:04:46 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Michael Murray Subject: Re: [Hanson] ln12 reading References: In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 933 Status: RO X-UID: 1022 X-Keywords: we thought the rationale for multiplying was pretty well motivated in section 4.2: that is, if we took the better motivated version of independence given in 4.2, then we instantly derive the initial, multiplication version. The multiply version is technically preferable, because it works even for zero-probability events. Take another look at sect 4.2 and let me know if you're still not satisfied with the explanation. regards, A. Michael Murray wrote: > I found it surprising that the independence equation was Pr(A n B) = > Pr(A).Pr(B). > > My original thought was that the A and B would be independent if Pr(A > u B) = Pr(A) + Pr(B), this would imply that there is no overlap in > the sets A and B and so they would be independent. I am not sure > where this intuition fails and why we instead look at the > intersection. What is the intuition behind multiplying two > probabilities? > > Michael Murray From crowell@MIT.EDU Wed Nov 23 11:15:11 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 jANGFB5o014070 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 11:15:11 -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 jANGFA7H006796 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 11:15:10 -0500 (EST) Received: from [18.238.6.73] (EASTCAMPUS-EIGHT-FORTY.MIT.EDU [18.238.6.73]) (authenticated bits=0) (User authenticated as crowell@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANGEjqt025708 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 11:15:03 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v734) Content-Transfer-Encoding: 7bit Message-Id: <17A1589D-CDD3-4659-90A7-884E8DE12846@mit.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Robert Crowell Subject: [Hanson] Reading comments Date: Wed, 23 Nov 2005 11:14:42 -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: 1023 Content-Length: 246 X-Keywords: Hi, I'd like to see a little more about A Posteriori probabilities in class. I'm having some trouble understanding how to work backwards and arrive at some answer, like the Halting Problem example on page 18, section 3.4 --Rob Crowell From meyer@imap.theory.csail.mit.edu Wed Nov 23 11:17:51 2005 Message-ID: <43849631.8050307@csail.mit.edu> Date: Wed, 23 Nov 2005 11:17:53 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Harrison King Hall Subject: Re: [David] Week 12 Comments References: In-Reply-To: Content-Type: text/plain; charset=ISO-2022-JP Content-Transfer-Encoding: 7bit Content-Length: 968 Status: RO X-UID: 1024 X-Keywords: events are SETS (of outcomes), so A$B"A(BB is the intersection of events A and B. It consists of those outcomes in both A and B, so A$B"A(BB is typically referred to as "the event that both A and B occur". make sense? regards, A. Harrison King Hall wrote: > David- > Wow, I know nothing about probability. Well not absolutely nothing, > but close enough for the rigor required by this course. By far the > most interesting case in probability that I had not even considered > was Posteriori probabilities. I had always heard and made phrases like > that, but now I understand where the mathematical basis is from. I > realize it is only a special case of conditional probability, but I > think it is awesome. The most difficult thing for me for a long time > was independence since I didn't find a rigorous definition of Pr{A $B"A(B > B} in the notes. Maybe it was there but I didn't catch it for a while > and I am still a little fuzzy on it. > -Harrison From meyer@imap.theory.csail.mit.edu Wed Nov 23 11:29:50 2005 Message-ID: <438498FF.3020100@csail.mit.edu> Date: Wed, 23 Nov 2005 11:29:51 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Harrison King Hall Subject: Re: [David] Week 12 Comments References: In-Reply-To: Content-Type: text/plain; charset=ISO-2022-JP Content-Transfer-Encoding: 7bit Status: RO Content-Length: 969 X-UID: 1025 X-Keywords: events are SETS (of outcomes), so A$B"A(BB is the intersection of events A and B. It consists of those outcomes in both A and B, so A$B"A(BB is typically referred to as "the event that both A and B occur". make sense? regards, A. Harrison King Hall wrote: > David- > Wow, I know nothing about probability. Well not absolutely nothing, > but close enough for the rigor required by this course. By far the > most interesting case in probability that I had not even considered > was Posteriori probabilities. I had always heard and made phrases like > that, but now I understand where the mathematical basis is from. I > realize it is only a special case of conditional probability, but I > think it is awesome. The most difficult thing for me for a long time > was independence since I didn't find a rigorous definition of Pr{A $B"A(B > B} in the notes. Maybe it was there but I didn't catch it for a while > and I am still a little fuzzy on it. > -Harrison From cvnguyen@MIT.EDU Wed Nov 23 11:32:41 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 jANGWf5o019961 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 11:32:41 -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 jANGW185025423 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 11:32:40 -0500 (EST) Received: from MULTIVAC (EASTCAMPUS-SIX-SIXTY.MIT.EDU [18.238.5.149]) (authenticated bits=0) (User authenticated as cvnguyen@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANG3xjJ021224 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 11:04:01 -0500 (EST) Message-ID: <039201c5f047$859f21b0$9505ee12@addressisp.com> From: "Chieu Nguyen" To: <6042-probs@theory.lcs.mit.edu> Subject: [Jelani] Week 12 comments Date: Wed, 23 Nov 2005 11:03:54 -0500 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Spam-Score: -1.215 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1026 Content-Length: 181 X-Keywords: I found the Monty Hall example interesting, amusing, and entertaining. It's a good example of how often people rely on intuition rather than reasoning out the problem. --Chieu From cbossard@MIT.EDU Wed Nov 23 11:53:41 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 jANGrf5o006408 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 11:53:41 -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 jANGrd7H021125 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 11:53:40 -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 jANGrbEZ011052 for <6042-probs@theory.lcs.MIT.EDU>; Wed, 23 Nov 2005 11:53:37 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-4.mit.edu (8.12.4) id jANGrbtd030995; Wed, 23 Nov 2005 11:53:37 -0500 Received: from pool-141-156-39-164.res.east.verizon.net (pool-141-156-39-164.res.east.verizon.net [141.156.39.164]) (User authenticated as cbossard@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Wed, 23 Nov 2005 11:53:37 -0500 Message-ID: <20051123115337.v75luc9tqym8488g@webmail.mit.edu> Date: Wed, 23 Nov 2005 11:53:37 -0500 From: cbossard@MIT.EDU To: 6042-probs@theory.lcs.MIT.EDU Subject: [David] Week 12 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: 1027 Content-Length: 266 X-Keywords: NonJunk I found this to be a very interesting reading because probability is an interesting topic. I don't have any specific questions on any one section in particular because I have been at least somewhat introduced to all of these topics in my probability class. Cynthia From hmzhou@blackbird.csail.mit.edu Wed Nov 23 12:12:26 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 jANHCQ5o015845; Wed, 23 Nov 2005 12:12:26 -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 jANHCP5L002915; Wed, 23 Nov 2005 12:12:25 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jANHCPoK002912; Wed, 23 Nov 2005 12:12:25 -0500 Date: Wed, 23 Nov 2005 12:12:25 -0500 (EST) From: Hanson Zhou To: Michael Murray cc: 6042-probs@theory.csail.mit.edu Subject: Re: [Hanson] ln12 reading In-Reply-To: Message-ID: References: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1028 Content-Length: 850 X-Keywords: Addition would mean that the events are mutually exclusive. Independence is different. Intuitively, event A and event B are independent means that A occurring affects B occurring not at all, and vice versa. Thus, we can compute Pr[A and B] by simply multiplying Pr[A]Pr[B], ie consider the probability of each event occurring separately. -Hanson On Wed, 23 Nov 2005, Michael Murray wrote: > I found it surprising that the independence equation was Pr(A n B) = > Pr(A).Pr(B). > > My original thought was that the A and B would be independent if Pr(A > u B) = Pr(A) + Pr(B), this would imply that there is no overlap in > the sets A and B and so they would be independent. I am not sure > where this intuition fails and why we instead look at the > intersection. What is the intuition behind multiplying two > probabilities? > > Michael Murray > From hmzhou@blackbird.csail.mit.edu Wed Nov 23 12:29:18 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 jANHTH5o025703; Wed, 23 Nov 2005 12:29:17 -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 jANHTH7m003064; Wed, 23 Nov 2005 12:29:17 -0500 Received: from localhost (hmzhou@localhost) by blackbird.csail.mit.edu (8.13.4/8.13.4/Submit) with ESMTP id jANHTHSZ003061; Wed, 23 Nov 2005 12:29:17 -0500 Date: Wed, 23 Nov 2005 12:29:17 -0500 (EST) From: Hanson Zhou To: Karena Tyan cc: 6042-probs@theory.lcs.MIT.EDU Subject: Re: [Hanson] Reading Comments 12 In-Reply-To: <20051123014503.5lactfb6xr4kowcs@webmail.mit.edu> Message-ID: References: <20051123014503.5lactfb6xr4kowcs@webmail.mit.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Status: RO X-UID: 1029 Content-Length: 1285 X-Keywords: Yes...independence for two variables is also mutual independence for two variables. It is true that the two probabilities are related...in fact they are related by precisely the formula for conditional probability that you wrote. The point is that often it is easy to compute one and not the other. For example, to compute Pr[A|B], you can compute Pr[A n B] and Pr[B] using a tree diagram and then use the formula to find Pr[A|B]. -Hanson On Wed, 23 Nov 2005, Karena Tyan wrote: > Just for clarification (this isn't my main question), two events that are > independent are *also* mutually independent, by the definition of independence > and mutual independence, correct? (pages 23-25) > > I am confused about the a posteriori probability covered in pages 17-18. In the > tutor problem 12.2, it is said that Pr{A} = 0.8 and Pr{L} = 0.4; in a case like > this, how would you compute Pr{L|A} without being given that it is 0.3? I > mean, I know that Pr{L|A} = Pr{A n L}/Pr{L}, but A n L is dependent upon the > value of Pr{A|L}, which is in turn dependent upon the value of Pr{L|A} in that > Pr{A|L} = Pr{A n L}/Pr{L}. In general, I'm just a little confused over how to > find A n B or Pr{A|B}. > > - Karena > > -- > 410 Memorial Drive > Cambridge, MA 02139 > (585)957-5923 > From dshin@MIT.EDU Wed Nov 23 12:54:51 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 jANHsp5o030095 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 12:54:51 -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 jANHsnSK026591; Wed, 23 Nov 2005 12:54:49 -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 jANHsjMu023547; Wed, 23 Nov 2005 12:54:46 -0500 (EST) Message-ID: <4384ACE2.2030105@mit.edu> Date: Wed, 23 Nov 2005 12:54:42 -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 12 Comments References: In-Reply-To: Content-Type: text/plain; charset=ISO-2022-JP 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: 1030 Content-Length: 960 X-Keywords: A $B"A(B B is just an event. For example, if we are considering the roll of a die, and A is the event "roll a 1, 3 or 5", and B is the event "roll a 2, 3, or 4", then A $B"A(B B is the event "roll a 3". Hope that helps DS Harrison King Hall wrote: > David- > Wow, I know nothing about probability. Well not absolutely nothing, > but close enough for the rigor required by this course. By far the > most interesting case in probability that I had not even considered > was Posteriori probabilities. I had always heard and made phrases like > that, but now I understand where the mathematical basis is from. I > realize it is only a special case of conditional probability, but I > think it is awesome. The most difficult thing for me for a long time > was independence since I didn't find a rigorous definition of Pr{A $B"A(B > B} in the notes. Maybe it was there but I didn't catch it for a while > and I am still a little fuzzy on it. > -Harrison From mitras@theory.csail.mit.edu Wed Nov 23 12:56:19 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 jANHuJ5o030250 for <6042-probs@theory.lcs.mit.edu>; Wed, 23 Nov 2005 12:56:19 -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 jANHuISK026651; Wed, 23 Nov 2005 12:56:18 -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 jANHuAok013859; Wed, 23 Nov 2005 12:56:11 -0500 (EST) Message-ID: <4384AD3A.40406@theory.csail.mit.edu> Date: Wed, 23 Nov 2005 12:56:10 -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: Timothy Mwangi CC: 6042-probs@theory.lcs.mit.edu Subject: Re: [Sayan] Week 12 Comments References: <6.2.1.2.2.20051123082057.03a06eb0@po12.mit.edu> In-Reply-To: <6.2.1.2.2.20051123082057.03a06eb0@po12.mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: -0.74 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1031 Content-Length: 808 X-Keywords: If you think of probabilities as functions attaching values in [0,1] to sets in the sample space (events), then this is not so surprising. The notion of time, (and therefore the notions of past and future) is not a part of the probability model. It just so happens that sometimes we attach more meaning to the events, like order them in time, for our convenience. The probability is just a function on the sets, does not matter if the sets "correspond" to events in the past or the future. Best, Sayan Timothy Mwangi wrote: > > Passage: 3.4 A Posteriori Probabilities > Page: 17 > I found this passage most surprising because of the notion that we > could use probability to say not only what will happen in the future > but what happened in the past. > > Sincerely, > Timothy M. Mwangi From dshin@MIT.EDU Wed Nov 23 12:56:26 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 jANHuQ5o030256 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 12:56:26 -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 jANHuPb2019868 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 12:56:25 -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 jANHuOgS028600; Wed, 23 Nov 2005 12:56:24 -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 jANHuCok013860; Wed, 23 Nov 2005 12:56:13 -0500 (EST) Message-ID: <4384AD39.5090206@mit.edu> Date: Wed, 23 Nov 2005 12:56:09 -0500 From: David Shin User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Sergio Bacallado CC: 6042-probs@theory.csail.mit.edu Subject: Re: [David] Week 12 Comments References: <5.2.1.1.2.20051122220644.00c3e5e8@po14.mit.edu> In-Reply-To: <5.2.1.1.2.20051122220644.00c3e5e8@po14.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: 1032 Content-Length: 520 X-Keywords: In fact, the outcome space can be infinite! In subsequent lectures, we should be seeing ways to avoid such a brute-force "identify all outcomes" strategy. DS Sergio Bacallado wrote: > I found the topic of independence very interesting. I wonder if there > is a simpler way to determine independence between events, because > evaluating the probabilities of intersections for every possible > subset of outcomes must become cumbersome as the outcome space becomes > very large. > > Sergio Bacallado > Group A. > From dshin@MIT.EDU Wed Nov 23 12:57:25 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 jANHvP5o030406 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 12:57:25 -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 jANHvOb2021234 for <6042-probs@theory.csail.mit.edu>; Wed, 23 Nov 2005 12:57:24 -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 jANHrOgS028498; Wed, 23 Nov 2005 12:53:25 -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 jANHrGok013724; Wed, 23 Nov 2005 12:53:17 -0500 (EST) Message-ID: <4384AC89.7070802@mit.edu> Date: Wed, 23 Nov 2005 12:53:13 -0500 From: David Shin User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Chris Yang CC: 6042-probs@theory.csail.mit.edu Subject: Re: [David] Week 12 Comments References: <200511230117.jAN1H4mA021113@outgoing.mit.edu> In-Reply-To: <200511230117.jAN1H4mA021113@outgoing.mit.edu> Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: 8bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1033 Content-Length: 613 X-Keywords: Yes...assuming that the "given" event corresponds to a single nice sub-path down the tree (that's not always the case). DS Chris Yang wrote: > Quick question regarding conditional probability: is asking the > probability of something given another event the same as the > probability of that something happening using all the probabilities on > the subtree after that “another” event? Hm, that is a difficult > question to ask in e-mail form. Assuming an event is given – is that > equivalent to, say, traversing down one path on the tree of that given > event? > > Have a good break! > > -Chris Yang > From meyer@imap.theory.csail.mit.edu Wed Nov 23 12:47:45 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 jANHlh5o028515 for <6042-staff@theory.csail.mit.edu>; Wed, 23 Nov 2005 12:47:43 -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 jANHlgb2007245 for <6042-staff@theory.csail.mit.edu>; Wed, 23 Nov 2005 12:47:42 -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 jANHlggS028178; Wed, 23 Nov 2005 12:47:42 -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 jANHlcMu023093; Wed, 23 Nov 2005 12:47:38 -0500 (EST) Message-ID: <4384AB39.3000602@theory.csail.mit.edu> Date: Wed, 23 Nov 2005 12:47:37 -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: Jon Stritar , 6042 staff <6042-staff@theory.csail.mit.edu> Subject: Re: [Sayan] Reading comments References: <1132758760.19347.2.camel@localhost.localdomain> In-Reply-To: <1132758760.19347.2.camel@localhost.localdomain> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: -2.599 X-Scanned-By: MIMEDefang 2.42 X-Spam-Checker-Version: SpamAssassin 2.63 (2004-01-11) on theory.csail.mit.edu X-Spam-Level: X-Spam-Status: No, hits=-4.9 required=3.7 tests=BAYES_00 autolearn=ham version=2.63 Status: RO Content-Length: 383 X-UID: 1034 X-Keywords: Glad you appreciate this systematic approach. -sayan Jon Stritar wrote: >1.3 Step 1: Find the Sample Space > >I always think its amazing how important this step is for me to write >down. Once I have the sample space down, and in the correct format for >the problem, (like a tree, table, or all the events written out), the >solution emerges quite naturally. > >Jon Stritar > > > From meyer@imap.theory.csail.mit.edu Wed Nov 23 14:16:50 2005 Return-Path: Received: from rozz.csail.mit.edu (mail@rozz.csail.mit.edu [128.30.2.16]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jANJGn5o012875 for ; Wed, 23 Nov 2005 14:16:49 -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 1Ef06r-0007tL-NP for meyer@csail.mit.edu; Wed, 23 Nov 2005 14:16:49 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jANJGmW4004056; Wed, 23 Nov 2005 14:16:48 -0500 (EST) Received: from [18.96.6.116] (SIMMONS-THREE-SEVENTY-ONE.MIT.EDU [18.96.6.116]) (authenticated bits=0) (User authenticated as hkhall@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jANJGfQk027542 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT); Wed, 23 Nov 2005 14:16:41 -0500 (EST) In-Reply-To: <438498FF.3020100@csail.mit.edu> References: <438498FF.3020100@csail.mit.edu> Mime-Version: 1.0 (Apple Message framework v623) Content-Type: text/plain; charset=ISO-2022-JP; format=flowed Message-Id: <8c3ccf380da4c59ae306e8babc47e1c1@mit.edu> Cc: David D Shin From: Harrison King Hall Subject: Re: [David] Week 12 Comments Date: Wed, 23 Nov 2005 14:16:40 -0500 To: "Prof. Albert R. Meyer" X-Mailer: Apple Mail (2.623) X-Spam-Score: 1.217 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 Content-Length: 1333 X-UID: 1035 X-Keywords: I finally got it on the tutor problems after doing it 4 or 5 different ways and getting different answers each time, then I reverse engineered the meaning from that. David emailed me as well and I think I got the formal definition now. Thanks for all of the help. See you in class today. -Harrison On Nov 23, 2005, at 11:29 AM, Prof. Albert R. Meyer wrote: events are SETS (of outcomes), so A$B"A(BB is the intersection of events A and B. It consists of those outcomes in both A and B, so A$B"A(BB is typically referred to as "the event that both A and B occur". make sense? regards, A. Harrison King Hall wrote: > David- > Wow, I know nothing about probability. Well not absolutely nothing, > but close enough for the rigor required by this course. By far the > most interesting case in probability that I had not even considered > was Posteriori probabilities. I had always heard and made phrases like > that, but now I understand where the mathematical basis is from. I > realize it is only a special case of conditional probability, but I > think it is awesome. The most difficult thing for me for a long time > was independence since I didn't find a rigorous definition of Pr{A $B"A(B > B} in the notes. Maybe it was there but I didn't catch it for a while > and I am still a little fuzzy on it. > -Harrison From mukkala@MIT.EDU Mon Nov 28 14:37:57 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jASJbv5o004382 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 14:37:57 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jASJbtDC025710 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 14:37:55 -0500 (EST) Received: from PRAVEENPAMIDI.mit.edu (KS-ONE-FIFTY-TWO.MIT.EDU [18.235.1.152]) (authenticated bits=0) (User authenticated as mukkala@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jASJbqba027382 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 14:37:53 -0500 (EST) Message-Id: <6.2.1.2.2.20051128140633.03e5fa00@po12.mit.edu> X-Mailer: QUALCOMM Windows Eudora Version 6.2.1.2 Date: Mon, 28 Nov 2005 14:38:02 -0500 To: 6042-probs@theory.csail.mit.edu From: Praveen Pamidimukkala Subject: [Sayan] Week 12 Comments Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1037 Content-Length: 355 X-Keywords: In section 4.3 of the Course Notes on Probability, disjointness is mentioned in comparison to independence. I understand that mathematically, when two events are disjoint, Pr{AintB} = 0 as opposed to Pr{AintB} = Pr{A} x Pr{B}, which applies for independence. However, in terms of events, how could this be described? Thanks, Praveen Pamidimukkala From hzhou@MIT.EDU Mon Nov 28 18:12:32 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jASNCW5o003459 for <6042-probs@theory.lcs.mit.edu>; Mon, 28 Nov 2005 18:12:32 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jASNCV3o018516 for <6042-probs@theory.lcs.mit.edu>; Mon, 28 Nov 2005 18:12:31 -0500 (EST) Received: from hzhou.mit.edu (BURTON-SIX-TWENTY-FOUR.MIT.EDU [18.247.7.113]) (authenticated bits=0) (User authenticated as hzhou@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jASNCCpc009185 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NOT) for <6042-probs@theory.lcs.mit.edu>; Mon, 28 Nov 2005 18:12:24 -0500 (EST) Message-Id: <5.2.1.1.2.20051128181100.02b043b8@po9.mit.edu> X-Sender: hzhou@hesiod X-Mailer: QUALCOMM Windows Eudora Version 5.2.1 Date: Mon, 28 Nov 2005 18:12:15 -0500 To: 6042-probs@theory.lcs.mit.edu From: Steven Zhou Subject: David-tp13 reading comment Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii"; format=flowed X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1038 Content-Length: 144 X-Keywords: NonJunk Hey, Reading and lecture were clear. I found the ability to get a percentage confidence for sampling data to be interesting. - Steven Zhou From icharny@MIT.EDU Mon Nov 28 19:19:41 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT0Jf5o021596 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 19:19:41 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT0Je3o003544 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 19:19:40 -0500 (EST) Received: from w92-130-webmail-5.mit.edu (W92-130-WEBMAIL-5.MIT.EDU [18.7.22.136]) ) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT0JbOW024603 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 19:19:38 -0500 (EST) Received: (from nobody@localhost) by w92-130-webmail-5.mit.edu (8.12.4) id jAT0Jb5R027958; Mon, 28 Nov 2005 19:19:37 -0500 Received: from ab6.draper.com (ab6.draper.com [192.80.95.243]) (User authenticated as icharny@ATHENA.MIT.EDU) by webmail.mit.edu (Horde MIME library) with HTTP for ; Mon, 28 Nov 2005 19:19:37 -0500 Message-ID: <20051128191937.pl45v83e6tdwgcgk@webmail.mit.edu> Date: Mon, 28 Nov 2005 19:19:37 -0500 From: Isaac Charny To: 6042-probs@theory.csail.MIT.EDU Subject: [Sayan] Week 13 Comments MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 7bit User-Agent: Internet Messaging Program (IMP) H3 (4.0.3) X-Spam-Score: -2.599 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1039 Content-Length: 121 X-Keywords: NonJunk I don't understand binomial distribution (section 3.4, page 11). Please discuss this in the next lecture. ~Isaac Charny From a_lopez@MIT.EDU Mon Nov 28 19:51:40 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT0pe5o001999 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 19:51:40 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT0pJ3o023281 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 19:51:20 -0500 (EST) Received: from [18.234.1.61] (DP-SIXTY-ONE.MIT.EDU [18.234.1.61]) (authenticated bits=0) (User authenticated as a_lopez@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT0pCVM001023 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 19:51:13 -0500 (EST) Message-ID: <438BA605.10505@mit.edu> Date: Mon, 28 Nov 2005 19:51:17 -0500 From: Adriana Lopez User-Agent: Mozilla Thunderbird 1.0 (Windows/20041206) X-Accept-Language: en-us, en MIME-Version: 1.0 To: 6042-probs@theory.csail.mit.edu Subject: [Jelani] week 13 reading Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1040 Content-Length: 612 X-Status: A X-Keywords: NonJunk The section on polling was very confusing, I haven't quite understood it yet. I would like this to be explained better in class. There are a lot of variables and equations and it's hard to follow. I forgot what the goal of all this was by the fourth paragraph, and had to reread it a couple of times to understand why each equation brought us closer to what we wanted. Also, in the tutor problems, there was a question that included the concept of variance, but this was not mentioned in the notes (or at least I couldn't find it). This made it a lot more difficult to solve the problem. Adriana From cwong08@MIT.EDU Mon Nov 28 22:02:53 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT32r5o029585 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 22:02:53 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT32paG014663 for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 22:02:52 -0500 (EST) Received: from w20-575-41.mit.edu (W20-575-41.MIT.EDU [18.187.0.60]) (authenticated bits=56) (User authenticated as cwong08@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT32jfL028697 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NOT) for <6042-probs@theory.csail.MIT.EDU>; Mon, 28 Nov 2005 22:02:46 -0500 (EST) Received: (from cwong08@localhost) by w20-575-41.mit.edu (8.12.9) id jAT32jO5021918; Mon, 28 Nov 2005 22:02:45 -0500 Subject: [Sayan] Week 13 Comments From: Christopher Wong To: 6042-probs@theory.csail.MIT.EDU Content-Type: text/plain Content-Transfer-Encoding: 7bit Date: Mon, 28 Nov 2005 22:02:45 -0500 Message-Id: <1133233365.21884.1.camel@w20-575-41.mit.edu> Mime-Version: 1.0 X-Mailer: Evolution 2.0.4 X-Spam-Score: 3.816 X-Spam-Level: *** (3.816) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1041 Content-Length: 74 X-Keywords: I would like the approximation methods of page 13 explained more clearly. From ajshafer@MIT.EDU Mon Nov 28 23:02:17 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT42H5o025524 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 23:02:17 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT3wFdI021982 for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 23:02:16 -0500 (EST) Received: from ajshafer (AJSHAFER.MIT.EDU [18.247.4.109]) (authenticated bits=0) (User authenticated as ajshafer@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT3vw9K014618 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Mon, 28 Nov 2005 22:57:58 -0500 (EST) Message-ID: <000201c5f499$15955910$6d04f712@ajshafer> From: "Andrew Shafer" To: <6042-probs@theory.csail.mit.edu> Subject: [Sayan] Week 13 Comments Date: Mon, 28 Nov 2005 22:57:56 -0500 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2670 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2670 X-Spam-Score: -1.215 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1042 Content-Length: 336 X-Keywords: NonJunk Will we be going over those horrible equations for confidence in class? They are still pretty confusing even in the notes. Thanks, Andrew ---------------------------- Illegitmitatum Non Carborundum Est Andrew Shafer, MIT Blog http://shaferandrew.blogspot.com Si hoc legere scis numium eruditionis habes. ---------------------------- From yangc@MIT.EDU Tue Nov 29 01:01:10 2005 Return-Path: Received: from biscayne-one-station.mit.edu (BISCAYNE-ONE-STATION.MIT.EDU [18.7.7.80]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT61A5o018236 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 01:01:10 -0500 Received: from outgoing.mit.edu (OUTGOING-AUTH.MIT.EDU [18.7.22.103]) by biscayne-one-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT618bP004349 for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 01:01:09 -0500 (EST) Received: from christope8f0c6 (MACGREGOR-ONE-TWENTY-FOUR.MIT.EDU [18.239.5.124]) (authenticated bits=0) (User authenticated as yangc@ATHENA.MIT.EDU) by outgoing.mit.edu (8.13.1/8.12.4) with ESMTP id jAT6151v008182 (version=TLSv1/SSLv3 cipher=RC4-MD5 bits=128 verify=NOT) for <6042-probs@theory.csail.mit.edu>; Tue, 29 Nov 2005 01:01:06 -0500 (EST) Message-Id: <200511290601.jAT6151v008182@outgoing.mit.edu> From: "Chris Yang" To: <6042-probs@theory.csail.mit.edu> Subject: [David] Week 13 Comments Date: Tue, 29 Nov 2005 01:03:06 -0500 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_002F_01C5F480.A8A39050" X-Mailer: Microsoft Office Outlook, Build 11.0.5510 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcX0qpELJrydoAhpS0me67xMhEI4gg== X-Spam-Score: 0.179 X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1043 Content-Length: 2330 X-Keywords: NonJunk This is a multi-part message in MIME format. ------=_NextPart_000_002F_01C5F480.A8A39050 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable For the derivation of the confidence interval stuff, why can we assume p = =3D =BD to continue the calculations for delta? Is it because delta is like the upper bound on the error, and not the error itself? =20 Thanks, Chris Yang=20 ------=_NextPart_000_002F_01C5F480.A8A39050 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable

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

 

Thanks,

Chris Yang

------=_NextPart_000_002F_01C5F480.A8A39050-- From hsoumare@MIT.EDU Tue Nov 29 01:47:52 2005 Return-Path: Received: from south-station-annex.mit.edu (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by theory.csail.mit.edu (8.12.10/8.12.1) with ESMTP id jAT6lq5o026081 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 01:47:52 -0500 Received: from central-city-carrier-station.mit.edu (CENTRAL-CITY-CARRIER-STATION.MIT.EDU [18.7.7.72]) by south-station-annex.mit.edu (8.12.4/8.9.2) with ESMTP id jAT6lp8B027797 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 01:47:51 -0500 (EST) Received: from outgoing-legacy.mit.edu (OUTGOING-LEGACY.MIT.EDU [18.7.22.104]) by central-city-carrier-station.mit.edu (8.12.4/8.9.2) with ESMTP id jAT6lpi4026773 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 01:47:51 -0500 (EST) Received: from [18.241.6.6] (NEW-TWO-SIXTY-ONE.MIT.EDU [18.241.6.6]) ) by outgoing-legacy.mit.edu (8.12.4/8.12.4) with ESMTP id jAT6lhok023583 for <6042-probs@theory.lcs.mit.edu>; Tue, 29 Nov 2005 01:47:44 -0500 (EST) Mime-Version: 1.0 (Apple Message framework v746.2) Content-Transfer-Encoding: 7bit Message-Id: <59496C9D-DE34-4E43-9C8F-AFB9E97D5BD5@mit.edu> Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed To: 6042-probs@theory.lcs.mit.edu From: Hamidou Soumare Subject: {Sayan} Weekly Email Comment Date: Tue, 29 Nov 2005 01:57:19 -0500 X-Mailer: Apple Mail (2.746.2) X-Spam-Score: 1.217 X-Spam-Level: * (1.217) X-Spam-Flag: NO X-Scanned-By: MIMEDefang 2.42 Status: RO X-UID: 1044 Content-Length: 205 X-Keywords: NonJunk Hi, I didnt quite understand the section on polling and would like to have it gone over in class in more detail, especially the part about the confidence interval and its derivation. Thanks. Hamidou From meyer@imap.theory.csail.mit.edu Tue Nov 29 02:19:04 2005 Message-ID: <438C00E8.1040103@csail.mit.edu> Date: Tue, 29 Nov 2005 02:19:04 -0500 From: "Prof. Albert R. Meyer" Organization: MIT CSAIL User-Agent: Mozilla Thunderbird 1.0.6 (Windows/20050716) X-Accept-Language: en-us, en MIME-Version: 1.0 To: Adriana Lopez CC: 6042-probs@theory.csail.mit.edu Subject: Re: [Jelani] week 13 reading References: <438BA605.10505@mit.edu> In-Reply-To: <438BA605.10505@mit.edu> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Content-Length: 808 Status: O X-UID: 1045 X-Keywords: Variance crept in by accident; will be covered next week. I've revised the tutor problem to indicate this. Thanks for pointing this out. regards, A. Adriana Lopez wrote: > The section on polling was very confusing, I haven't quite understood > it yet. I would like this to be explained better in class. There are > a lot of variables and equations and it's hard to follow. I forgot > what the goal of all this was by the fourth paragraph, and had to > reread it a couple of times to understand why each equation brought us > closer to what we wanted. > Also, in the tutor problems, there was a question that included the > concept of variance, but this was not mentioned in the notes (or at > least I couldn't find it). This made it a lot more difficult to solve > the problem. > Adriana