If you have a bivariate normal, then the marginals are normal and the mean and variance of X, and Y too,
have to be the same as they were in the joint distribution.
The conditional is also normal and can be found in http://en.wikipedia.org/wiki/Multiva...l_distribution
Look under ...Conditional distributions... they even give you the mean and variance of Y|X.
So for X|Y just switch your random variables.