Let X1, X2, . . . be a sequence of independent and identically distributed continuous random variables.

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}.