Let x1nbspx2 frac14 xnnbspdenote the elements of a gaussian

Question

Let X_1, X₂, ¼, X_n 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

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