Question: (20 pts) Let X be a continuous, nonnegative random variable, that is f(x) = 0 for x < 0. Show that E[X] = (1

(20 pts) Let X be a continuous, nonnegative random variable, that is f(x) = 0 for x < 0. Show that E[X] = (1 Fx(x))d, where Fx(x) is the cdf of X. (2) 8X (Hint:) Consider integrating by parts. The following fact is helpful: if E(X) exists thenlim x x[1 F(x)] = 0.

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