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As stated in the title, I am looking for the solution to this expectation, possibly as a function of $\rho$. One relevant solution I find is Lord Shark the Unknown's answer, from which I can derive $E(max(X, Y)) = \frac{1}{2}E(|V|)$. But I am not sure what to do next. Any suggestions?

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  • $\begingroup$ If $X$ and $Y$ have zero means and unit variances, then you might follow this answer:math.stackexchange.com/questions/382237/…. $\endgroup$ – StubbornAtom Aug 1 '18 at 19:09
  • $\begingroup$ Actually, in your linked post the OP has answered your question. $\endgroup$ – StubbornAtom Aug 1 '18 at 19:16
  • $\begingroup$ @StubbornAtom Indeed! My fault. Thank you. $\endgroup$ – Yi Bao Aug 1 '18 at 19:28

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