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Y be an independent exponential random variable. 3 (20 points) Let X be a uniform random variable on [0, 1], and let Y be an

Y be an independent exponential random variable.

3 (20 points) Let X be a uniform random variable on [0, 1], and let Y be an independen ponential random variable with parameter 1. a) (10 points) Find the joint p.d.f. of U = Y - X and V = XY. b) (10 points) Find P(U 2 1). -by/62-4ac

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