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Quiz dossier / The Matrix Cookbook

08 - Gaussians

Advanced formula selection, assumption checking, and exact application for Gaussians, book pages 40-45.

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Question 1

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Affine Gaussian transformations

Let x∼N(mu,Sigma)x\sim N(mu,Sigma) and y=Ax+by=Ax+b.

ValidInvalidStatement
E[y]=Amu+bE[y]=Amu+b
Cov(y)=ASigmaATCov(y)=A Sigma A^T
yy is Gaussian
Cov(y)=ASigma+bCov(y)=A Sigma+b