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317.Uniform Sums Past ln 2

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expected valueCh. 6 — Random Variables and Expectation444+ Problems in Probability
Let X1,X2,…X_1, X_2, \dots be IID Unif(0,1)\mathrm{Unif}(0,1) and let N=min⁡{n:X1+⋯+Xn>ln⁡2}N = \min\{n : X_1 + \cdots + X_n > \ln 2\}. Find E[N]E[N].

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