This exercise demonstrates that the multivariate distributio
Question and Solution
This exercise demonstrates that the multivariate distribution with maximum entropy, for a given covariance, is a Gaussia
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This exercise demonstrates that the multivariate distribution with maximum entropy, for a given covariance, is a Gaussian. The entropy of a distribution p(x) is given by H[x] = ? p(x) ln p(x) dx. (2.279) We wish to maximize H[x] over all distributions p(x) subject to the constraints that p(x) be normalized and that it have a specific mean and covariance, so that p(x) dx = 1 (2.280) p(x)x dx =
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