4. Let X'= (X₁,..., Xn) be an n-dimensional random vector whose covariance matrix exists. Let A be an m x n matrix ofconstants. Then Cov(AX) = ACov(X)A'. True or false, give reasoning.

Let's simplify Covariance of AX, Cov(Ax)= E[(Ax-E(Ax))(Ax-E(Ax))]' = E[(Ax-A*E(x))(Ax-A*E(x))]'

Answered: 4. Let X'= (X₁,..., Xn) be an…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 13EQ

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4. Let X'= (X₁,..., Xn) be an n-dimensional random vector whose covariance matrix exists. Let A be an m x n matrix of constants. Then Cov(AX) = ACov(X)A'. True or false, give reasoning.