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# N (15pts) Let X be a random variable with universe of outcomes 12. Let P(2) be...

## Question

###### N (15pts) Let X be a random variable with universe of outcomes 12. Let P(2) be... n (15pts) Let X be a random variable with universe of outcomes 12. Let P(2) be a collection of subsets of the power set of 12 for which a probability function Prob() is defined. Assume that A = A1 and the finite collection of sets {A;}, for i = 1 to n are such that the following two conditions hold. a U A; = 2; b If i # j, then A; n A; = 0. With this, prove that Bayes' theorem becomes the statement that Prob(BA1)Prob(A1) Prob(A1\B) = Prob(B|A;)Prob(A;) i=1 n j=1

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