Quick question on bivariate normal distribution please: I know for a bivariate normal distribution, the two variables are marginally normal and all the conditional distributions are also normal. Is the reverse true? i.e. if you have two random variables that are marginally normal themselves and all the conditional distributions of one variable given a value of the other are also normal, does this result in the joint distribution has to be "bivariate normal" or it can still be another type of joint distribution? thanks.