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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

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