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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