Question: 10. Suppose X is a Gaussian random variable with mean [1. and covariance matrix 2, in n dimensions. a. Let B be an n X

10. Suppose X is a Gaussian random variable with mean [1. and covariance matrix 2, 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 coefcients can be arranged into Y = X'AX where A is an n X n symmetric matrix. b. Find E(X'AX). C. E(BX'AX)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

please provide steps 10. Suppose X is a Gaussian random Mariab h mean f and covariance matrix E. in n dimensions. a. Let B be an n x in real matrix The scalar random variable } = X'BX is referred to...

please give steps 10. Suppose X is a Gaussian random variable with mean / and covariance matrix E, in n dimensions. a. Let B be an n x n real matrix. The scalar random variable Y = X'BX is referred...

Implement in Python the Naive Bayes model discussed in lecture for the MNIST dataset. h(x) = argmax_kappa epsilon{0, 1, ..., 9} [fx| kappa(x)P[Y = k]]. = argmax_kappa elementof{0, 1, ...,...

Probability and statistics. 1. A survey of people in given region showed that 25% drank regularly. The probability of death due to liver disease, given that a person drank regularly, was 6 times the...

Before applying any algorithm to a real - world problem, it is common practice to first understand its behavior on synthetic data. Let s generate a synthetic data set for a regression problem: given...

Page 1 of 9 SIT787 -Mathematics for Al Assignment 3 Related to the content of Weeks 6-10 Trimester 2, 2024 Important notes: e Submission deadline can be found on the unit website. Your submission can...

8.6.3 Positively Correlated Normal Test Statistics Assume that (bS1; : : : ; bSm) is distributed according to a N (m;S)-Gaussian distribution, with Si j 0 for all i; j = 1; : : : ;m. We want to test...

Let Y=(Y1,Y2,Y3,) be a random vector with mean vector and covariance matrix given by m = (1 , -1 , 3) and Cov (Y) = 1 1 0 1 2 3 0 3 10 a. Let Z1= Y1 + Y2 + Y3, Z2 = 3Y1 +Y2 +Y3 Find for Z=(Z1,Z2) i....

2 CS229 Problem Set #4 Solutions log m ! p(x(i) |)p() = log p() + m " log p(x(i) |) i=1 i=1 = log p() + m " log " p(x(i) , z (i) |) log " Qi (z (i) ) i=1 = log p() + log p() + m " z (i) i=1 z (i) m...

Question: Prompt: Submit a comprehensive risk analysis paper that identifies the cyberlaw foundations that affect Equifax. The framework for the assessment will include how the business model ensures...

For some odd reason, you decide to throw baseballs at a car of mass M, which is free to move frictionlessly on the ground. You throw the balls at the back of the car at speed u, and at a mass rate of...

Following information has been obtained from the books of Habanaltd: Selling price per unit R10 Variable cost per unit R6 Total Fixed cost R60 000 Required: Calculate the following, round off units...

E2-40B Determine whether information is relevant (Learning Objective 6) Classify each of the following costs as relevant or irrelevant to the decision at hand and briefly explain your reason. a. The...

During Opportunity Identification, what tools might we incorporate to provide information? PIC Customer site visits All of These Cumulative Expenditures Curve

3.3 Describe the impact that HRtechnology has on the role of the HR professional and the resulting three major changes to the role of HR.

3. How has the workplace failed at securing equal opportunities or wages for women?

2. Why do we need legislation to protect women in the workplace?