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5. The pdf of the exponential distribution is f (x) = where 0 and 9 > O. Suppose X and Y are two independent random vari- ables distributed exponentially with parameter O = 1. a. Derive the joint and marginal densities of U = 2(X + Y) and V = X/ Y. (Note that the reverse transformations are X = [JV/2(V + 1) and Y = b. Show that [land Vare independent.