Question: Q3. Suppose that X is a Gamma distributed random variable with parameters a and 1. Additionally, Y is uniform on (0,1) and that X and

Q3. Suppose that X is a Gamma distributed random variable with parameters a and 1. Additionally, Y is uniform on (0,1) and that X and Y are independent. a) Compute the variance of Z = XY b) Compute the moment generating function (mgt) of W = X + Y

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