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)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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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?
Transcribed Image Text: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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