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/
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa81eeb4a-8e20-493f-a2a6-05e80f069cf7%2Fc87c97e9-78be-4e12-ab25-94b5112c92a2%2Fkhcxwf_processed.jpeg&w=3840&q=75)
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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