Answer to Question #336722 in Statistics and Probability for alvin

Question #336722

Let X and Y be two independent random variables having joint probability density function f(x, y) = 1/ 2πσ2 e − (x−µ) 2 σ2 e − (y−µ) 2 σ2 − ∞ < x, y < ∞

Find the moment generating function of Z = X+Y /2 and hence the mean and variance of Z


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