Correlation of X and Max(X,Y) - Quant Trader Interview Question
Difficulty: Hard
Category: Market Microstructure
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Topics: probability, correlation, normal-distribution, expected-value, mental-math
Problem Description
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.
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