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Suppose that (X,Y) are bivariate normal with non-zero means and correlation. Is there any neat expression for $\mathbb{E}(X|Y>0)$?

Ferdi
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Egor
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    Since $\mathbb{E}[X|Y=y]=\rho y$, what about integrating $\rho y$ over the positive half-line? – Xi'an May 10 '15 at 19:15
  • @Xi'an I think the nonzero means need to be taken into account too. – Dilip Sarwate May 10 '15 at 20:27
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    @Xi'an So, you mean to use $\mathbb{E}[X|Y>0] = \mathbb{E}[\mathbb{E}(X|Y)|Y>0]$? Thanks a lot. – Egor May 11 '15 at 08:49
  • https://stats.stackexchange.com/questions/385423/multivariate-normal-expectation-of-x-given-y-is-doubly-truncated?noredirect=1&lq=1, https://stats.stackexchange.com/questions/356023/expectation-of-truncated-normal/ – StubbornAtom Mar 06 '19 at 13:32

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