## Multivariate Normal conditional tail Expextation

Hi all,
I need help regarding the following expression:
E(x1|X>K)
where:
x1 is a one dimension normal rv
X is multivariate normal rv with n components: x1, x2,..., x_n
K is a n dimension constant vector with n components: k1,k2,...,k_n
X>K <==> x1>k1,x2>k2,...,x_n>k_n

I know there is a closed form for the Bi-variate case. Is there one for this too?

Thanks a lot!

Alon