Hello,

Sorry I won't write it in Latex, I hope it will be enough.

The mean of a variable is not a variable anymore. It is a constant.

And so is the variance of a variable.

Now there are 2 properties of the mean and the variance. If a is a constant, then :

E{a}=a and Var{a}=0.

Hence E{Var(X|Y)}+Var{E(X|Y)}=Var(X|Y)+0=Var(X|Y)

So... is there some missing information or a mistake somewhere ? :s