3. If X and Y are discrete random variables, each taking only two distinct values, prove that X and Y are independent if and only if E(XY) = E(X)E(Y).
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Three random variables A, B, and C are independent if and only if the joint probability distribution of A, B, and C can be expressed as the product of their marginal probability distributions, i.e., P(A=a, B=b, C=c) = P(A=a) * P(B=b) * P(C=c) for all possible Show more…
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