Let S be the sample space of an experiment. Let A and B be

Chapter , Problem 22

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Let S be the sample space of an experiment. Let A and B be two events of S. Let IA and IB be the indicator variables for A and B. That is, IA() = B 1 if A 0 if , A, IB() = B 1 if B 0 if , B. Show that IA and IB are positively correlated if and only if P (A | B) > P (A), and if and only if P (B | A) > P (B).

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