# Conditional moments of bivariate normal

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

• 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
• @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 8:49
• – StubbornAtom Mar 6 '19 at 13:32