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Correlation of X and Max(X,Y)

Hard · Market Microstructure · Quant Trader interview question · probability, correlation, normal-distribution, expected-value, mental-math

Let $X$ and $Y$ be independent standard normal random variables. Define $M = \max(X, Y)$. What is the correlation between $X$ and $M$? Assume all relevant quantities exist and are well-defined. No calculators or external resources are allowed.