# How to obtain mean and joint distribution in factor analysis?

I have a factor analysis model defined by:

$x = m + Wz + e$

where $x$ is a p-dimensional visible variable, $m$ is a constant vector, and $z$ is a $n$-dimensional Gaussian latent variable with $z$ ~ $N(0, I)$, $W$ is a $p\times m$ matrix and $e$ is a $p$-dimensional with $e$ ~ $N(0, \Psi$) - it is the factor loadings matrix. $Z$ and $e$ are independent.

$p(x)$ is defined by the model is Gaussian, but how do I find its mean?

Also, what is the explicit joint distribution of $p(z, x)$?

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You keep reusing the same letters for different meanings ($m, p$), but the mean of $x$ is clearly $m$, because the rest have mean $0$. –  Aniko Apr 27 '12 at 21:24
Peter, you need to take a crash course in multivariate normal distribution and do some exercises to understand the derivations involved. This was discussed on CV before, and you can also find helpful handouts from various multivariate statistics classes. –  StasK Jun 26 at 13:17