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Question: 2. Let X and Y be independent random variables with X ~ Gamma(a, 1) and Y ~ Garnma(3, 1) Consider…

by Essaynice Tutors | Sep 9, 2023 | statistics and probability

Question: 2. Let X and Y be independent random variables with X ~ Gamma(a, 1) and Y ~ Garnma(3, 1) Consider...

Show transcribed image text 2. Let X and Y be independent random variables with X ~ Gamma(a, 1) and Y ~ Garnma(3, 1) Consider the transformation U = X-r and V = NT. a) Find the joint pdf of U and V. b) Find the marginal pdf of U. c) Find the marginal pdf of V d) Show that U and V are independent.

2. Let X and Y be independent random variables with X ~ Gamma(a, 1) and Y ~ Garnma(3, 1) Consider the transformation U = X-r and V = NT. a) Find the joint pdf of U and V. b) Find the marginal pdf of U. c) Find the marginal pdf of V d) Show that U and V are independent.