# Question

Let X1, X2, . . . be a sequence of independent and identically distributed continuous random variables. Let N ≥ 2 be such that

X1 ≥ X2 ≥ . . . ≥ XN−1 < XN

That is, N is the point at which the sequence stops decreasing. Show that E[N] = e.

First find P{N ≥ n}.

X1 ≥ X2 ≥ . . . ≥ XN−1 < XN

That is, N is the point at which the sequence stops decreasing. Show that E[N] = e.

First find P{N ≥ n}.

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