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 $p(z, x)$?