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A random variable T~ gamma (a,^) has density function: (^t)a-1, + >o a) show that it belongs to an exponential family. Define neutral parameters as functions of a and λ. -1t ле fy(t) = f(a) 10² гса) b) let X,~ Gamma (a, 1) and X₂ ~ Gamma (agil) be independent random variables. Let Y₁ = x, and Y₂ = X₁ + X₂ Find the marginal probability density functions for Y₁ and 1₂ Are they independent? ex/

A random variable T~ gamma (a,^) has density function: (^t)a-1, + >o a) show that it belongs to an exponential family. Define neutral parameters as functions of a and λ. -1t ле fy(t) = f(a) 10² гса) b) let X,~ Gamma (a, 1) and X₂ ~ Gamma (agil) be independent random variables. Let Y₁ = x, and Y₂ = X₁ + X₂ Find the marginal probability density functions for Y₁ and 1₂ Are they independent? ex/

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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A random variable T~ gamma (a,^) has density function fy(t) = plas r(a) ле -1t 0<7' 1-6 (76) a) show that it belongs to an exponential family. Define neutral parameters as functions of a and a. let X,~ Gamma (a,, 1) and X₂ ~ Gamma (921) be independent random variables. Lex Y₁ = X₁/X₂ and Ya =X₁ + X₂. Find the marginal probability density functions for Y₁ and Y2 Are they independent?
Transcribed Image Text:A random variable T~ gamma (a,^) has density function fy(t) = plas r(a) ле -1t 0<7' 1-6 (76) a) show that it belongs to an exponential family. Define neutral parameters as functions of a and a. let X,~ Gamma (a,, 1) and X₂ ~ Gamma (921) be independent random variables. Lex Y₁ = X₁/X₂ and Ya =X₁ + X₂. Find the marginal probability density functions for Y₁ and Y2 Are they independent?
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