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Expected Value of the k-th Smallest

Hard · Probability & Statistics · Quant Trader interview question · probability, expected-value, order-statistics, uniform-distribution

Suppose you generate $n$ independent random numbers from a uniform distribution between 0 and 1. Let $X_{(k)}$ denote the $k$-th smallest of these numbers. What is the expected value of $X_{(k)}$? In other words, what is $EX_{(k)}$?