Question: Let X be a random variable that takes on nonnegative values and has distribution function F(x). Show that Hint: Integrate by parts. Illustrate this result

Let X be a random variable that takes on nonnegative values and has function F(x). Show that

Hint: Integrate by parts. Illustrate this result by calculating E(X) by this method if X has an exponential F(x) = 1 − e−λx for x ≥ 0, and F(x) = 0 otherwise.

E(X)=(1-F(x))dz . 0

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Integrating by parts we have EX xdF 2 z1 Fx 1 F2x 1F 1 Fxdx To justify this argment we have to sho... View full answer

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