Chapter 3 Random Vectors and Multivariate Normal …
Uncorrelated implies independence for multivariate normal random vari-ables 9. IfX, μ,andΣarepartitionedasabove, thenX1 andX2 areindependent if and only if Σ12 =0=ΣT 21. Proof. We will use m.g.f to prove this result. Two random vectors X1 and X2 are independent iff M(X 1,X2)(t1,t2)=MX 1 (t1)MX 2 (t2). Chapter 3 93
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