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

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2.21. Let X and Y be independent Bernoulli (1/2) random variables. Let Z =
(Y – X)². What is the distribution of Z? Show that Z and X are independent.
Show that Z and Y are also independent, but that X, Y and Z are not independent.
Transcribed Image Text:2.21. Let X and Y be independent Bernoulli (1/2) random variables. Let Z = (Y – X)². What is the distribution of Z? Show that Z and X are independent. Show that Z and Y are also independent, but that X, Y and Z are not independent.
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