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Expected Maximum of n Uniforms

Asked atJane StreetAkuna Capital

Question

Let U1,…,UnU_1, \dots, U_n be independent Uniform(0,1)\text{Uniform}(0,1) random variables, and let M=max⁡iUiM = \max_i U_i.

Find E[M]E[M], and give the intuition for the answer in one sentence.

Solution

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