8. (30 pts) Given two RVs X and Y. Compute the pdf of (a) W = X + Y, \\ (b) W = min(X, Y), (c) W = max(X, Y), in terms of their joint pdf \\ fxy(x, y).
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Let f_{X,Y}(x,y) denote the given joint pdf of X and Y. For each W (a function of X and Y) compute the CDF F_W(w)=P(W ≤ w) as an appropriate double integral of f_{X,Y}, then differentiate F_W(w) with respect to w (using Leibniz rule) to obtain the pdf f_W(w). Show more…
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