So, the problem gives me this facts (for a Normal bivariate distribution X,Y)
$$Var(Y|X=x) = 5$$ $$E(Y|X=x) = 2 + x$$
It asks me to find $$E[Y^2|X=7]$$
I tried this: using the conditional variance $$Var[Y|X=x] = E[Y^2|X=x] + E[Y|X=x]^2 $$ So, $$ E[Y^2|X=x] = Var[Y|X=x] - E[Y|X=x]^2$$ $$ E[Y^2|X=x] = 5 - (2 + x)^2$$ Evaluating in X = 7, $$ E[Y^2|X=7] = 5 - (9)^2$$ $$ E[Y^2|X=7] = -76$$
Am I wrong? where?