1) If X and Y are normal random variables with E(X) = 1, E(X^2) = 5, E(Y) = −1, Var(Y) = 4 and Corr(X, Y ) = −1/2, then what is E[X | Y = 1]?

I know Var(X) = 5-1 = 4, SD(X) = 2, but don't know what to do from there...


2) I know that if (X,Y) is bivariate normal, then the following formulas hold.
 E(Y|X=x) \, = \, E(Y) \, + \, \frac{Cov(X,Y)}{V(X)} \cdot \left[x \, - \, E(X) \right]
 Var[Y|X=x] = (1-\rho^2) Var Y
But what if we only know that X and Y are normal (NOT necessarily bivariate normal), are these formulas still true? Why or why not?

Thanks for any help!