Question: 7. Let X1, X2, . . . be independent, identically distributed, continuous random variables. Define N as the index such that X1 X2

7. Let X1, X2, . . . be independent, identically distributed, continuous random variables. Define N as the index such that X1 ≥ X2 ≥ · · · ≥ XN−1 and XN−1 < XN .

Prove that P(N = k) = (k − 1)/k! and that E(N) = e.

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