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.
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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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constants. Then Cov(AX) = ACov(X)A'. True or false, give reasoning."
Transcribed Image Text: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.
Expert Solution
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Step 1:-
Let's simplify Covariance of AX,
Cov(Ax)= E[(Ax-E(Ax))(Ax-E(Ax))]'
= E[(Ax-A*E(x))(Ax-A*E(x))]'
Step by step
Solved in 2 steps
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