I would like to get a precise answer to this question, I can't seem to find a clear answer anywhere.
Moreover, what about this special case :
I have $m$ gaussian random variables $X_i$ ($i=1,...,m$), which are dependent because they are defined by
$$ X_1 = X - a_1\\ X_2 = X - a_2\\ \vdots\\ X_m = X - a_m, $$
where the $a_i$ are real positive constants and $X$ is a random variable following $N(\mu, \sigma^2)$.
So they all have the same variance, but not the same mean. Is their joint distribution a multivariate gaussian? And if not, what can I say about their joint distribution?
Thanks a lot.