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# Class Note for MATH 3338 at UH

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COURSE
PROF.
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TYPE
Class Notes
PAGES
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WORDS
KARMA
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## Popular in Department

This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15
Math 3338 Probability Fall 2006 Jiwen He Section Number 10853 http math uh eduj iwenhemath3338fa1106 html Jiwen He UrWErsity er Huustun jiwenhemam uh Edu Mam 333E Prubabmty FaH zane September 11 7 September 15 was Probability p14 25 Independence mwen HE Umversm er Huustun jwwenhemam uh Edu Mam 3333 Prubabmty FaH zane September 11 7 September 15 was Probablllty p24 Definition of independent events 0 Definition Two events A and B are independent if PABgt PM and are dependent otherwise 0 The equality in the de nition implies the following equality and vice versa P B IA 133 o It is also straightforward to show that if A and B are independent then so are the following pairs of events 1 A and B 2 A and B and 3 A and B o 231 Tossing adieA 246 B 123and0 1234 We have PA PAB PAC That is A and B are dependent whereas A and C are independent 0 232 Let A and B be mutually exclusive with PA gt 0 Since A n B I then PAB 0 7 PA so A and B can not be independent For example A carisblue and B carisred A and B are mutually exclusive then dependent m JiWEn He UrWErsity er Heusteniiwennemam uh Edu Mam 333E Prubahiiity Faii mus September 11 7 September 15 was Probability p34 PA m B When A and B are Independent 0 Proposition A and B are independent if and only if PA F B PA PB 0 Proof PA B PAB PB PA PB where the second equality is valid if and only if A and B are independent 0 Definition of the independence of more than two events Events A1 An are mutually independent if for every k k 2 3 n and every subset of indices 2391 0k PAii quot39 A7 kPAi1quot39PAik o 235 Let Ar denote the event that the lifetime of cell 239 exceeds to i 1 6 We assume that Ai s are independent events and that PAi 9 for every 239 since the cells are identical 1 Psystem lifetime exceeds to PA1 A2 A3 U A4 A5 A6 PA1 AQ HA3 lPA4 A5 HA6 PA1 A2 A3 A4 A5 A6 H 999 999 999999 927 Jiwen He University of Houston jiwenhemathuhedu Math 3338 Probability Fall 2006 September 11 September 15 2006 Probability p44

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