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

2259_Equation 02.jpg

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

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