# Product of Two Multivariate Gaussian Distributions

I asked a question with a similar title before, but I phrased it incorrectly so I am reposting.

What is the mean and covariance of the distribution, $f_{PA}(PA) \cdot f_{Y|X,PA}(Y)$ where $f_{PA}$ and $f_{Y|X,PA}$ are both gaussian distributions? (The distribution over $X,Y,PA$ is Gaussian.) $Y,PA$ are vectors.

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Why not edit the original question instead of posting a new one? I think you should delete this one and edit the original. – Dilip Sarwate Nov 3 '12 at 3:44