I'm sure that the following question is trivial, but I can't found a solid demonstration.
Can we state that multi-factor model is a multivariate gaussian distribution?
multi-factor model:
X_ij = sigma_i * Z_i + sqrt(1-sigma_i^2)* E_ij
where
i=1,...,k
j=1,...,n_i
0 < sigma_i <...