Let X and Y be independent random variables each taking the values 1 and –1 with probability 1/2. (a) Prove that X and XY are independent. (b) Prove that X, XY and Y are not (jointly) independent.
Let X and Y be independent random variables each taking the values 1 and –1 with probability 1/2. (a) Prove that X and XY are independent. (b) Prove that X, XY and Y are not (jointly) 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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![Let X and Y be independent random variables each taking the values 1
and –1 with probability 1/2.
(a) Prove that X and XY are independent.
(b) Prove that X, XY and Y are not (jointly) independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa290310a-dd9c-431f-9c5c-6815758e2d5d%2F194190aa-d62a-4f6b-8516-264db750109c%2Ftwlic7_processed.png&w=3840&q=75)
Transcribed Image Text:Let X and Y be independent random variables each taking the values 1
and –1 with probability 1/2.
(a) Prove that X and XY are independent.
(b) Prove that X, XY and Y are not (jointly) independent.
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