Prove theorem 213theorem 213the multivariate normal random, Ask an Expert

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Prove Theorem 2.13.

THEOREM 2.13

The multivariate normal random variables X _I , X₂, . X_kare mutually independent if and only if they are pairwise uncorrelated. The proof consists of invoking Theorem 2.10 and using the moment generating function (Eq. 2.97) (see Exercise 2.1).

THEOREM 2.10

A set of multivariate normal variates X 1 , X2, . . . Xk are independent if and only if X is diagonal.

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