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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A: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question and…

Q: (i) the maximum value of p.d.f. (ii) expectation of X, E(X) (iii) variance of X.

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A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

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A: The joint probability function is fx, yx, y=2,   x≥0, y≥0, x+y≤10, otherwise

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A: The expected value is also known as average of the probability distribution function. It is the…