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$X,Y,Z$ are standard normal R.V.

What is the value of $\operatorname{E}[X|X+Y+Z=1]$ and $\operatorname{Var}(X|X+Y+Z=1)$?

I think the first one should be $1/3$ by symmetry but don't know how to tackle the second part.

Any thought on this? Thanks a lot!

3 Answers 3