I have the following joint distribution for the random variable (X,Y):
Now, I have to compute the following expectations:
- $E(X+Y^2 | Y)$
Now, for the first point, the procedure was the following:
But I don't know how to do the second one. Intuitively maybe I can write something like:
$E(X+Y^2 | Y) = E(X|Y) + E(Y^2 | Y)$
but I stopped here.
Edit 1: I forgot to specify that $x,y$ are positive.