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Question 2 Suppose X and Y are independent standard normal random variables. We wish to find the distribution of R= /X² + Y², the distance from the origin of the random point (X,Y). a) What is the distribution of Z = X² + Y²? What is its density? b) Use the cumulative distribution function method to find the density of R = VZ. This is called the Rayleigh distribution. [For partial credit, if you did not answer (a), write the density of R in terms of the density of Z and specify the range of R.]

Question 2 Suppose X and Y are independent standard normal random variables. We wish to find the distribution of R= /X² + Y², the distance from the origin of the random point (X,Y). a) What is the distribution of Z = X² + Y²? What is its density? b) Use the cumulative distribution function method to find the density of R = VZ. This is called the Rayleigh distribution. [For partial credit, if you did not answer (a), write the density of R in terms of the density of Z and specify the range of R.]

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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Question 2 Suppose X and Y are independent standard normal random variables. We wish to find the distribution of R= /X² + Y², the distance from the origin of the random point (X,Y). a) What is the distribution of Z = X² + Y²? What is its density? b) Use the cumulative distribution function method to find the density of R = VZ. This is called the Rayleigh distribution. [For partial credit, if you did not answer (a), write the density of R in terms of the density of Z and specify the range of R.]
Transcribed Image Text:Question 2 Suppose X and Y are independent standard normal random variables. We wish to find the distribution of R= /X² + Y², the distance from the origin of the random point (X,Y). a) What is the distribution of Z = X² + Y²? What is its density? b) Use the cumulative distribution function method to find the density of R = VZ. This is called the Rayleigh distribution. [For partial credit, if you did not answer (a), write the density of R in terms of the density of Z and specify the range of R.]
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