Homework Help is Here – Start Your Trial Now!
Math
Probability
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)
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...
See similar textbooks
icon
Related questions
Question
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.
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
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))]'

 

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer