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Suppose X₁ and X₂ are i.r.v. and come from gamma(2a, 2). Show that U = X₁ + X₂ comes from gamma(4a, 2). Using software R, sample from X₁, X₂ and U and confirm that U = X₁ + X2, where U~ gamma(4a, 2) and gamma(2a, 2) and X₂ ~ gamma(2a, 2). Use values a = 2 and λ = 3. X₁

Suppose X₁ and X₂ are i.r.v. and come from gamma(2a, 2). Show that U = X₁ + X₂ comes from gamma(4a, 2). Using software R, sample from X₁, X₂ and U and confirm that U = X₁ + X2, where U~ gamma(4a, 2) and gamma(2a, 2) and X₂ ~ gamma(2a, 2). Use values a = 2 and λ = 3. X₁

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose X₁ and X₂ are i.r.v. and come from gamma(2a, λ). Show that U = X₁ + X₂ comes from gamma(4a, 2). Using software R, sample from X₁, X₂ and U and confirm that U = X₁ + X₂, where U ~ gamma(4a, 2) and X₁ ~ gamma(2a, 2) and X₂ ~ gamma(2a, 2). Use values a = 2 and λ = 3.
Transcribed Image Text:Suppose X₁ and X₂ are i.r.v. and come from gamma(2a, λ). Show that U = X₁ + X₂ comes from gamma(4a, 2). Using software R, sample from X₁, X₂ and U and confirm that U = X₁ + X₂, where U ~ gamma(4a, 2) and X₁ ~ gamma(2a, 2) and X₂ ~ gamma(2a, 2). Use values a = 2 and λ = 3.
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