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TL;DR

Expected Maximum of Two Uniforms: A canonical quantitative trading interview question at foundation difficulty. Commonly asked at Two Sigma, Citadel, DE Shaw, Jump Trading.

By Valenke Exam Prep Team·Last updated 2026-06-01
foundationRandom Variables & Distributions

Expected Maximum of Two Uniforms

Asked at: Two Sigma, Citadel, DE Shaw, Jump Trading

Problem
Let XX and YY be independent uniform random variables on [0,1][0,1]. Find E[max⁡(X,Y)]E[\max(X, Y)]. Generalize: for nn independent Uniform(0,1)\text{Uniform}(0,1) random variables, what is E[max⁡(X1,…,Xn)]E[\max(X_1, \ldots, X_n)]?
Related concepts
Order Statistics

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