6. Let X1 and X2 be random variables such that(2e-e-#2 0 < #1 < x2 < o∞f(r1, 22) :otherwise.(a) What is the marginal pdf of X1?(b) Consider the random variables Y1 = 2X1 and Y2 = X2 – X1. Find the joint density of Y1 and Y2.(c) Are Y1 and Y2 independent? Why or why not?

Answered: Image /qna-images/answer/f930c15c-1314-4795-97fb-fe474a28a041.jpg

6. Let X1 and X2 be random variables such that 2e-#e=#20 < x1 < x2 < oo f(r1, T2) = otherwise. (a) What is the marginal pdf of X,? (b) Consider the random variables Yı = 2X1 and Y2 = X2 – X1. Find the joint density of Yı and Y2. (c) Are Y1 and Y2 independent? Why or why not?

6. Let X1 and X2 be random variables such that 2e-#e=#20 < x1 < x2 < oo f(r1, T2) = otherwise. (a) What is the marginal pdf of X,? (b) Consider the random variables Yı = 2X1 and Y2 = X2 – X1. Find the joint density of Yı and Y2. (c) Are Y1 and Y2 independent? Why or why not?

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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6. Let X1 and X2 be random variables such that
(2e-e-#2 0 < #1 < x2 < o∞
f(r1, 22) :
otherwise.
(a) What is the marginal pdf of X1?
(b) Consider the random variables Y1 = 2X1 and Y2 = X2 – X1. Find the joint density of Y1 and Y2.
(c) Are Y1 and Y2 independent? Why or why not?

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