Say i have two discrete rv's $X,Y$ and let y be a value Y can take on with non zero probability.
Is $Var(X|Y=y)$ given by:
$E((X|Y=y)^2)+E(X|Y=y)^2$ or by $E(X^2|Y=y)+E(X|Y=y)^2$
I believe that the two expressions are actually the same thing, is this correct?