conditional normal distribution proportional to a joint density?

Question

First of all, I am sorry if this is not the proper place to ask questions about statistics. I study Machine Learning so I wonder if there is a more appropriate website for this kind of questions.

I only wonder why a conditional gaussian p(x1|x2) is said to be proportional to the joint density where it comes from, p(x1, x2).

Thanks

Answer 1

a conditional gaussian p(x1|x2) is said to be proportional to the joint density where it comes from, p(x1, x2)

In a sense, every conditional density is proportional to the corresponding joint density, since p(x1 | x2) = p(x1, x2) / p(x2), so maybe that's what they mean; it's not a property which is special to the Gaussian distribution. However, that's not "proportional" in the usual sense, because the factor 1/p(x2) is not a constant.