Let X 1 , X 2 , , X n denote the elements of a Gaussian vector X The Z are independent with mean i and variance 2 i , i 1, 2, , n Show that the differential entropy of the vector X equals what does h(X) reduce to if the variances are equal h(X) log (2 mre(ofo o)...

The differential entropy of a random variable is independent of its mean To evalua ...

Let X 1 , X 2 , . . , X n denote the elements of a

Question:

Let X₁, X₂, . . , X_n denote the elements of a Gaussian vector X. The Z are independent with mean ?_i and variance ?²_i, i = 1, 2,. . . , n. Show that the differential entropy of the vector X equals what does h(X) reduce to if the variances are equal?