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455.The Last Bulb Standing

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expected valueCh. 6 — Random Variables and Expectation444+ Problems in Probability
Four lightbulbs have IID Exp(1)\mathrm{Exp}(1) lifetimes X1,X2,X3,X4X_1, X_2, X_3, X_4. Find the expected time until the last bulb burns out, E[max⁡iXi]E[\max_i X_i].

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