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special matrix in terms of its covariance matrix

How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...
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Modeling with a Bivariate Gaussian Distribution

In an earlier question I inquired about contour lines reflecting probability values in a Bivariate Gaussian Distribution. I have spent some time thinking and playing around with a Mathematica ...