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Correlation of Min and Max of Uniforms

Hard · Probability & Statistics · Quant Trader interview question · probability, correlation, uniform-distribution, expectation

Suppose you generate two independent random variables, $X$ and $Y$, each drawn from a uniform distribution on the interval $0, 1$. Let $U = \min(X, Y)$ and $V = \max(X, Y)$. What is the Pearson correlation coefficient between $U$ and $V$, $\rho(U, V)$?