Question: Notation: to consider a 'Gaussian' approximation of the d-dimensional unit sphere, by considering a Gaussian random vector X N (0, I/d), where I is the

Notation: to consider a 'Gaussian' approximation of the d-dimensional unit sphere, by considering a Gaussian random vector X N (0, I/d), where I is the d d identity matrix

LetARdd be any unitary matrix, ieATA=AAT=I Show that the pdf ofXN(0,I/d) and the pdf of X~=AXare the same, i.e they do not depend on the choice of A.

Thank you!

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!

Notation: to consider a 'Gaussian' approximation of the d-dimensional unit sphere, by considering a Gaussian random vector X N (0, I/d), where I is the d d identity matrix. This means that for large...

Notation: consider a 'Gaussian' approximation of the d-dimensional unit sphere, by considering a Gaussian random vector W N (0, I/d), where I is the d d identity matrix. If we draw two datapoints X,...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

In this question we will investigate how our intuition for samples from a Gaussian may break down in higher dimen- sions. Consider samples from a D-dimensional unit Gaussian x N(0D, ID) where 0p...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Solve all. 5 Consider the success run chain in Example 8.2.16. Suppose that the chain has been running for a while and is currently in state 10. (a) What is the expected number of steps until the...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Let X be a random variable with X~ N(, 02). The PDF of X is written explicitly as (2-) fx(x) = (1) (a) Let = 0 and o= 1 so that X ~ N(0,1). Plot fx (r) using matplotlib.pyplot.plot for the range...

Hi, math experts. I am recently learning from Pattern Recognition and Machine Learning, Chris Bishop. Please provide a detailed explainations briefly for the following sections. 1. Section 1.2.2...

K Compute the monthly payments for an add-on interest loan of $1450, with an annual interest rate of 8% and a term of 3 years. The monthly payment is S (Round to the nearest cent as needed.) REER

(a) If A is a matrix with three rows and five columns, then what is the maximum possible number of leading 1s in its reduced row echelon form? (b) If B is a matrix with three rows and six columns,...

Which of the following most accurabely describe the approach of the Democratic Party of Andrew lachoson as it relases to the lase of slimery? Aveided the lasue whenevtr posilt le Blamed slavery for...

A hardware store keeps records of the strength of lawn mower engines and their fuel usage. The scatter plot shows a line of fit, and the table shows the residuals. A scatter plot titled Lawn Mowers...