4. Let X and Y be independent, continuous random variables with densities {}} and fx(x) = fy (y) = = {}² if 0 < x < 2 otherwise. y if 0 < y < 2 otherwise. (a) Compute the density of X+Y. (b) Let Z = ¹ (X+Y) (that is, the Z is the average of X and Y). What is the density of Z?

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