Homework Help is Here – Start Your Trial Now!
Math
Statistics
Suppose X is a Gaussian random variable with mean u and covariance matrix D, in n dimensions. a. Let B be an n x n real matrix. The scalar random variable Y = X''BX is referred to as a quadratic form (in normal variables). Show that if B is not symmetric, its coefficients can be arranged into Y = X'AX where A is an n x n symmetric matrix. Find F(X'AX)

Suppose X is a Gaussian random variable with mean u and covariance matrix D, in n dimensions. a. Let B be an n x n real matrix. The scalar random variable Y = X''BX is referred to as a quadratic form (in normal variables). Show that if B is not symmetric, its coefficients can be arranged into Y = X'AX where A is an n x n symmetric matrix. Find F(X'AX)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
1
Suppose X is a Gaussian random variable with mean u and covariance matrix E, in n dimensions. a. Let B be an n x n real matrix. The scalar random variable Y to as a quadratic form (in normal variables). Show that if B is not symmetric, its coefficients can be arranged into Y = X'AX where A is an n x n symmetric X'BX is referred matrix. b. Find E(X'AX). c. E(eX'AX)
Transcribed Image Text:Suppose X is a Gaussian random variable with mean u and covariance matrix E, in n dimensions. a. Let B be an n x n real matrix. The scalar random variable Y to as a quadratic form (in normal variables). Show that if B is not symmetric, its coefficients can be arranged into Y = X'AX where A is an n x n symmetric X'BX is referred matrix. b. Find E(X'AX). c. E(eX'AX)
Expert Solution
steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS