Suppose that (X,Y) are bivariate normal with non-zero means and correlation. Is there any neat expression for $\mathbb{E}(X|Y>0)$?
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1$\begingroup$ Since $\mathbb{E}[X|Y=y]=\rho y$, what about integrating $\rho y$ over the positive half-line? $\endgroup$ – Xi'an May 10 '15 at 19:15
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$\begingroup$ @Xi'an I think the nonzero means need to be taken into account too. $\endgroup$ – Dilip Sarwate May 10 '15 at 20:27
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1$\begingroup$ @Xi'an So, you mean to use $\mathbb{E}[X|Y>0] = \mathbb{E}[\mathbb{E}(X|Y)|Y>0]$? Thanks a lot. $\endgroup$ – Egor May 11 '15 at 8:49
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$\begingroup$ stats.stackexchange.com/questions/385423/…, stats.stackexchange.com/questions/356023/… $\endgroup$ – StubbornAtom Mar 6 '19 at 13:32
