Lecture21. TheMultivariateNormalDistribution
2 whereDisadiagonalmatrixwithλ i’sdownthemaindiagonal.Setu=Bt,u=tB; then M Y (t)=exp(t µ)exp( 1 2 t BDB t) andBDB issymmetricsinceDissymmetric.SincetBDBt=uDu,whichisgreater than0exceptwhenu=0(equivalentlywhent=0becauseBisnonsingular),BDB is positivedefinite,andconsequentlyY isGaussian. Conversely,supposethatthemoment …
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