it's not just about convenience of math though that's a big part of it another big factor why gaussians are a reasonable thing to use is that in fact even if there's enough underlying factors it might really be a Gaussian the thing you're looking at about multivariate gaussians well here's what it looks like these are densities where X is now a vector so we again see a normalization happening up front which is has a determinant of Sigma in it Sigma is a symmetric matrix the covariance matrix and have X minus mu X