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= Let X and Y be independent Bernoulli(1/2) random variables. Let Z : (Y – X)². What is the distribution of Z? Show that X and Z are independent. Show that Y and Z are also independent, but that X, Y, and Z are not independent.

= Let X and Y be independent Bernoulli(1/2) random variables. Let Z : (Y – X)². What is the distribution of Z? Show that X and Z are independent. Show that Y and Z are also independent, but that X, Y, and Z are not independent.

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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**Problem Statement:** Let \( X \) and \( Y \) be independent Bernoulli(1/2) random variables. Let \( Z = (Y - X)^2 \). - What is the distribution of \( Z \)? - Show that \( X \) and \( Z \) are independent. - Show that \( Y \) and \( Z \) are also independent, but that \( X \), \( Y \), and \( Z \) are not independent.
Transcribed Image Text:**Problem Statement:** Let \( X \) and \( Y \) be independent Bernoulli(1/2) random variables. Let \( Z = (Y - X)^2 \). - What is the distribution of \( Z \)? - Show that \( X \) and \( Z \) are independent. - Show that \( Y \) and \( Z \) are also independent, but that \( X \), \( Y \), and \( Z \) are not independent.
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