Matrix distribution of scatter matrices with given covariance and degrees of freedom
WishartMatrixDistribution[ν, Σ]
Mean[WishartMatrixDistribution[3, DiagonalMatrix[{2, 1, 3}]]]//MatrixForm
→ MatrixForm[{{6, 0, 0}, {0, 3, 0}, {0, 0, 9}}]Variance[WishartMatrixDistribution[3, DiagonalMatrix[{2, 1, 3}]]]//MatrixForm
→ MatrixForm[{{24, 6, 18}, {6, 6, 9}, {18, 9, 54}}]