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Q3. Suppose that X is a Gamma distributed random variable with parameters a and 2. Additionally, Y is uniform on [0,1] and that X and

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Q3. Suppose that X is a Gamma distributed random variable with parameters a and 2. 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 (mgf) of W = X + Y

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