Denote the elements of a gaussian vector x

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Let X₁, X₂, ¼, X_n denote the elements of a Gaussian vector X. The X_i are independent with mean mi and variance , i = 1, 2, ¼, n. Show that the differential entropy of the vector X is given by

where e is the base of the natural logarithm.What does h(X) reduce to if the variances are all equal?

Reference no: EM131280080

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