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X and Y are independent standard normal random variables. What is the expected value of max(X, Y)?

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What is the expected value of the maximum of N independent normally distributed random variables?X and Y are independent standard normal samples (n observations each). You run the linear regression Y ~ X anyway. What is the expected value of R^2?Y and X1, ..., Xk are independent standard normal samples of n observations each. You run the linear regression of Y on X1, ..., Xk together. What is the expected value of R^2?

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