# Let X,Y be bivariate normal , what is E[X|Z] where Z = X + Y? [duplicate]

I am trying to understand how does expectation and variance looks when

Let X,Y be bivariate normal

I want understand E[X|Z] and Var[X|Z]

when Z = X + Y

• $(X,Z)$ is also bivariate normal, so $X$ given $Z$ is univariate normal. May 19 '21 at 12:18
• This is a FAQ: search our site for conditional normal expectation.
– whuber
May 19 '21 at 13:17