# post8 - STAT 511-2 Spring 2012 Lecture 8 Jan 27, 2012 Jun...

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1 STAT 511-2 Spring 2012 Lecture 8 Jan 27, 2012 Jun Xie Extra example on counting from the homework problem; Finish the definition of conditional probability and examples in the last post. 2.4 Conditional probability The multiplication rule Similarly, consideration of P(B|A) gives P ( A B ) = P(B|A)P(A). The multiplication rule is most useful when the experiment consists of several stages in succession. P ( A 1 A 2 A 3 ) = P ( A 3 | A 1 A 2 ) P ( A 1 A 2 ) = P ( A 3 | A 1 A 2 ) P ( A 2 | A 1 ) P ( A 1 ). Bayes’ Theorem Recall that events A 1 , . . . , A k are mutually exclusive if no two have any common outcomes. The events are exhaustive if one A i must occur, so that A 1 A k = S. The Law of Total Probability Let A 1 , . . . , A k be mutually exclusive and exhaustive events. Then for any other event B, P(B)=P(B|A 1 )P(A 1 )+…+ P(B|A k )P(A k ) Bayes’ Theorem Let A 1 , A 2 , . . . , A k be a collection of k mutually exclusive and exhaustive events with

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## This note was uploaded on 02/20/2012 for the course STAT 511 taught by Professor Bud during the Fall '08 term at Purdue University.

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post8 - STAT 511-2 Spring 2012 Lecture 8 Jan 27, 2012 Jun...

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