post9 - STAT 511-2 Spring 2012 Lecture 9 Jan 30, 2012 Jun...

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1 STAT 511-2 Spring 2012 Lecture 9 Jan 30, 2012 Jun Xie Review the Bayes theorem and go over examples. 2.5 Independence Definition Two events A and B are independent if P ( A | B ) = P ( A ) and are dependent otherwise. Proposition A and B are independent if and only if (iff) P ( A B ) = P ( A ) P ( B ) Example 34 It is known that 30% of a certain company’s washing machines require service while under warranty, whereas only 10% of its dryers need such service. If someone purchases both a washer and a dryer made by this company, what is the probability that both machines will need warranty service? Definition Events A 1 , . . . , A n are mutually independent if for every k ( k = 2, 3, . . . , n ) and every subset of indices i 1 , i 2 , . . . , i k , Example 36 Solar photovoltaic system Consider a particular lifetime value t 0 , and suppose we want to determine the probability that the system lifetime exceeds t 0 . Let A i denote the event that the lifetime of cell i exceeds t
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post9 - STAT 511-2 Spring 2012 Lecture 9 Jan 30, 2012 Jun...

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