I'm an undergraduate student. I read about multivariate normal distribution in hogg and craig. And i wonder why the covariance is allowed to be positive SEMI-definite. I read this
And I found this
I don't understand it actually. it talks about affine subspace or something. We still need the probability distribution to integrate out to 1. 1 is a real number, so what is the relation of that "affine subspace" with $R^n$?? Can anybody explain it in simple way? I am totally curious about this. Any illustration will be appreciated, Thanks..