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Let X = (X1, X2) be normally distributed random variables with mean m = (m1, m2) and covariance matrix S.

Y = max(X1, X2) = X1 + max(0, X2 - X1) = X1 + D (X2 - X1),

where D = 1 if X2 > X1 and 0 otherwise (bivariate).

What are E(Y) and Var(Y)? What if X1 and X2 are independent and what if X2 = c, a constant?

Thank you for sharing your brilliant insights into these matters!

kjetil b halvorsen
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KarlH
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    Related: https://stats.stackexchange.com/questions/229073/variance-of-maximum-of-gaussian-random-variables, https://stats.stackexchange.com/questions/381212/distribution-of-maximum-of-normally-distributed-random-variables, https://stats.stackexchange.com/questions/343914/expected-value-of-maximum-of-samples-from-normal-distribution, https://stats.stackexchange.com/questions/392183/expectation-of-max-of-two-normal-random-variables, https://stats.stackexchange.com/questions/139072/distribution-of-the-maximum-of-two-correlated-normal-variables – kjetil b halvorsen May 26 '21 at 23:07
  • ... you can find answers from those posts! – kjetil b halvorsen May 26 '21 at 23:09

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