The covariance matrix of a random vector is always positive semidefinite. Let e be the covariance…
The covariance matrix of a random vector is always positive semidefinite. Let e be the covariance matrix of the random vector X = (X1,…,xn) (not neces- sarily Gaussian). Show that is always positive semidefinite; i.e., Eq;a;Cij 20, for any a,…., , ER. i,k=1 Exercises 47 In particular, show that it is positive definite if and only if X is nondegenerate. Hint: Write the left side as the variance of some random variable. May 05 2022 06:05 PM
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