435.The Wait That Never Averages

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expected valueCh. 6 — Random Variables and Expectation444+ Problems in Probability

Let

U \sim \mathrm{Unif}(0,1)

and

X_1, X_2, \dots \sim \mathrm{Unif}(0,1)

IID, independent of

U

. Define

N = \min\{n : X_n > U\}

. Find

E[N]

. Enter

-1

if the answer is infinite.

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