What is the expected value of a truncated trivariate normal distribution?

Question

Specifically, if x, y, and z have a trivariate normal distribution, I am interested in E[x|y>a,z=b] and VAR[x|y>a,z=b] if a and b are constants. I have the formula for E[x|y>a] and E[x|y=a] for a bivariate normal distribution and was hoping there was an equally straightforward formula for the trivariate case.

Answer 1

It's not going to be equally straightforward since you're effectively increasing your arguments by an exponent. You can derive the formula, but it'd be a nightmare and take you almost as long as workign through it the hard way yourself.

Try Hogg and Tanis for a proof.