Homework Help is Here – Start Your Trial Now!
Math
Statistics
The binormal joint density function is

The binormal joint density function is

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

Hello,

Can you help me understand this problem? I have included the answer and can you give me in great detail how these were completed. I also included the answers

Problem 4.27: The binormal joint density function is 1 1 fx,y (x, y) exp 2(1 – p2) 2n0102/1- p2 [(r – m1)² of (y – m2)? 2p(x – m1)(y – m2)]| exp{-(z – m)C-'(z – m)'} (27)"det(C) where z = [r y], m = [m1 m2] and of C = c-( ) ρσισ 1) With c-() 4. C = 9 we obtain of = 4, o = 9 and pơ102 = -4. Thus 2) The transformation Z = 2X +Y, W = X – 2Y is written in matrix notation as ()-(: )G)-() 2 1 = A W The ditribution fz,w(z, w) is binormal with mean m' = mA', and covariance matrix C' = ACA'. Hence C' = ({ 9 2 2 4 -4 2 1 1 -2 9 -2 2 56 The off-diagonal elements of C' are equal to po zow = COV(Z,W). Thus COV (Z, W) = 2. 3) Z will be Gaussian with variance o? = 9 and mean %3D mz = [ m1 m2 = 4 21
Transcribed Image Text:Problem 4.27: The binormal joint density function is 1 1 fx,y (x, y) exp 2(1 – p2) 2n0102/1- p2 [(r – m1)² of (y – m2)? 2p(x – m1)(y – m2)]| exp{-(z – m)C-'(z – m)'} (27)"det(C) where z = [r y], m = [m1 m2] and of C = c-( ) ρσισ 1) With c-() 4. C = 9 we obtain of = 4, o = 9 and pơ102 = -4. Thus 2) The transformation Z = 2X +Y, W = X – 2Y is written in matrix notation as ()-(: )G)-() 2 1 = A W The ditribution fz,w(z, w) is binormal with mean m' = mA', and covariance matrix C' = ACA'. Hence C' = ({ 9 2 2 4 -4 2 1 1 -2 9 -2 2 56 The off-diagonal elements of C' are equal to po zow = COV(Z,W). Thus COV (Z, W) = 2. 3) Z will be Gaussian with variance o? = 9 and mean %3D mz = [ m1 m2 = 4 21
4.27 Random variables X and Y are jointly Gaussian with m = [1 2] -4 4 C = 9. 1. Find the correlation coefficient between X and Y. 2. If Z = 2X + Y and W = X – 2Y, find COV(Z, W). 3. Find the PDF of Z.
Transcribed Image Text:4.27 Random variables X and Y are jointly Gaussian with m = [1 2] -4 4 C = 9. 1. Find the correlation coefficient between X and Y. 2. If Z = 2X + Y and W = X – 2Y, find COV(Z, W). 3. Find the PDF of Z.
Expert Solution
steps

Step by step

Solved in 3 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