1. (a) Let X be a continuous, non-negative (that is, P(X ≥ 0) = 1) random variable with PDF f. Show that E(X) = ™P(X > x)dx. Hint: Note that P(X > x) = f f(y)dy. Substitute this into fo P(X> x)dx, and then switch the order of integration. Note: This is an analogue of the Tail Sum Formula for Expectation, proved in class for non-negative, integer-valued random variables.

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