Suppose that x is a random variable uniformly distributed in an ellipsoid \begin{equation} x^{T}Mx\leq\delta, \end{equation} where $x\in \mathbb{R}^{n}$. Clearly, the mean of $x$ is zero. The covariance matrix is given by \begin{equation} \frac{\delta}{(n+2)}M^{-1}. \end{equation} I want to know how to compute the covariance matrix. Anyone can give me some hint and references on it?
2026-04-08 22:45:12.1775688312
How to compute the covariance matrix of a random variable uniformly distributed in an ellipsoid
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