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The joint distribution of X and Y is given by

The joint distribution of X and Y is given by

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
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Hello, I know the answer to this question but I would like to understand how they got it and please explain it to me with the math in great detail. I also included the answer to this problem.

Problem 4.26: 1) The joint distribution of X and Y is given by 1 exp X fx.x(x, y) : xp{-3( x x ) 2πσ2 The linear transformations Z = X +Y and W = 2X – Y are written in matrix notation as (쥬)-(12)(주)-^(주) W = A Y Thus, (see Prob. 4.25) 1 fzw(z, w) : 2ndet(M) /2 exp{(z w)M-1 2тdet(M)1/2 W where M = A( )*- ( ) - ( ) 202 o2 Pz,wozow М— А o? 502 Pz,wozow From the last equality we identify o; = 20², o 50? and pz,w = 1//10
Transcribed Image Text:Problem 4.26: 1) The joint distribution of X and Y is given by 1 exp X fx.x(x, y) : xp{-3( x x ) 2πσ2 The linear transformations Z = X +Y and W = 2X – Y are written in matrix notation as (쥬)-(12)(주)-^(주) W = A Y Thus, (see Prob. 4.25) 1 fzw(z, w) : 2ndet(M) /2 exp{(z w)M-1 2тdet(M)1/2 W where M = A( )*- ( ) - ( ) 202 o2 Pz,wozow М— А o? 502 Pz,wozow From the last equality we identify o; = 20², o 50? and pz,w = 1//10
4.26 Let X and Y be independent Gaussian random variables, cach distributed accord- ing to N(0, o²). 1. Find the joint density function of the random variables Z = X + Y and W = 2X – Y. What is the correlation coefficient between these two random variables.
Transcribed Image Text:4.26 Let X and Y be independent Gaussian random variables, cach distributed accord- ing to N(0, o²). 1. Find the joint density function of the random variables Z = X + Y and W = 2X – Y. What is the correlation coefficient between these two random variables.
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