276.How Many Uniforms to Pass One
★★★expected valueJump Trading
Independent uniform (0,1) random variables are drawn one after another and added up. Let N be the first count at which the running total exceeds 1. What is the expected value of N?
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Use the tail formula for a non-negative integer variable, and note that the probability that n uniforms sum to at most 1 is the volume of a simplex.
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