Let X1,X2, . . . be a sequence of independent

Chapter 7, Problem 7.25

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Let X1,X2, . . . be a sequence of independent andidentically distributed continuous random variables.Let N 2 be such thatX1 X2 XN1 < XNThat is, N is the point at which the sequence stopsdecreasing. Show that E[N] = e.Hint: First find P{N n}.

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