\begin{eqnarray*}(adsbygoogle = window.adsbygoogle || []).push({});

&&\mathbb{E}\left( 1_{\left\{ X_{1}+X_{2}>\rho \right\} }X_{1}X_{2}\right)

\\

&&\mathbb{E}\left( 1_{\left\{ X_{1}+X_{2}>\rho \right\} }X_{1}^{2}\right)

\end{eqnarray*}

where ##X_1## and ##X_2## are independent normal variables. I am wondering whether there exist closed-form expressions for the above two expectations.

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# A Expectations of normal variables

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