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Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0) {: Ox0-1, 0 1, where 0 > 0 is unknown. Let 1 -0а-1 еxp(-0) r(a) f(0) be the prior distribution for 0, where a > 0 is a known constant, I(-) is the gamma function defined as I(a) = Jo xª-'e° dx for a > 0.

Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0) {: Ox0-1, 0 1, where 0 > 0 is unknown. Let 1 -0а-1 еxp(-0) r(a) f(0) be the prior distribution for 0, where a > 0 is a known constant, I(-) is the gamma function defined as I(a) = Jo xª-'e° dx for a > 0.

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) Find the posterior distribution for 0. Hint: the pdf of Y ~ Gamma(a, B) is f(y| a, B) = Ba r(a)ya-l exp (-By) for y > 0. 1
Transcribed Image Text:(a) Find the posterior distribution for 0. Hint: the pdf of Y ~ Gamma(a, B) is f(y| a, B) = Ba r(a)ya-l exp (-By) for y > 0. 1
Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0) {: Ox0-1, 0<x <1, x < 0 or x > 1, where 0 > 0 is unknown. Let 1 -0а-1 еxp(-0) r(a) f(0) be the prior distribution for 0, where a > 0 is a known constant, I(-) is the gamma function defined as I(a) = Jo xª-'e° dx for a > 0.
Transcribed Image Text:Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0) {: Ox0-1, 0<x <1, x < 0 or x > 1, where 0 > 0 is unknown. Let 1 -0а-1 еxp(-0) r(a) f(0) be the prior distribution for 0, where a > 0 is a known constant, I(-) is the gamma function defined as I(a) = Jo xª-'e° dx for a > 0.
Expert Solution
Step 1

We have given that

Let X 1 ,...,X n be a random sample from a population with probability density function  

f(x/θ)=θxθ-1  0<x<1

And the prior distribution of θ is 

f(θ)=1/αθα-1exp(-θ) 

The We have to find the posterior distribution of θ: 

 

 

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