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See image below for question. If X and Y are independent random variables and g and h are real-valued functions such that E(g(X)) and E(h(Y))

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If X and Y are independent random variables and g and h are real-valued functions such that E(g(X)) and E(h(Y)) exist and are finite, prove that E(g(X) h(Y)) = E(g(X)) E(h(Y)). For consis- tency, please assume X and Y are jointly continuous with joint pdf fx,y. Thanks

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