I have a random vector $\mathbf{X} \sim \mathcal{N}(\mathbf{m,\Sigma})$ which is transformed by a Gaussian Radial Basis Function into the random variable $\mathbf{Y} = K(\mathbf X)$ where $K = \exp(-\lambda||\mathbf X||^2)$ is there an analytic expression for the mean and variance of this new variable?
2026-04-02 15:58:07.1775145487
RBF transformation on a Normally Distributed Random Variable
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