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.
