1 Suppose X is a Gaussian random variable with mean u and covariance matrix E, in ndimensions.a. Let B be an n x n real matrix. The scalar random variable Yto 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 symmetricX'BX is referredmatrix.b. Find E(X'AX).c. E(eX'AX)

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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)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 14EQ

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