Recent content by lequan

\begin{eqnarray*} &&\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...

It seems that we need to get involved in a hypergeometric function, but no more detailed references...

Please help give references on solving the following integral: \int\frac{1}{c_{1}e^{ax}+c_{2}e^{bx}}dx where a\neq b Thanks a lot in advance.

Thanks a lot for the reference! This is the right answer. Actually, this is about the conditional distribution of multivariate normal variables, and well known in any standard textbook of basic statistics. However, I failed to realize this early. :(

X (n by 1) follows a multivariate normal distribution, i.e., X ~ N(mu, Sigma). mu is n by 1, Sigma is n by n. What is E(X|X_{sub}=A)? where the index 'sub' (m by 1) is a subset of {1,2,..,n}, A is m by 1, 1 <= m < n.