Let X~N(1,1), Y~N(2,1) be bivariate normal with cov(X,Y)=1/2. Obtain E(Y|X).
I see that you can get E(XY) using the covariance, but I don't see where that leads. The only way I know to calculate the conditional expectation is by integrating over the density function of Y given X, which is so ugly in this case that there's certainly an easier approach.