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Derive the posterior distribution for 1 given (x1, ...,x7) up to a proportional constant.

Derive the posterior distribution for 1 given (x1, ...,x7) up to a proportional constant.

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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Derive the posterior distribution for 1 given (x1,... ,xn) up to a proportional constant.
Transcribed Image Text:Derive the posterior distribution for 1 given (x1,... ,xn) up to a proportional constant.
Suppose we draw an i.i.d. sample X1, ...,X, from a Poisson(1) distribution, where l is a parameter of unknown value. The pdf of the Poisson(1) distribution is f(xi) x;! Suppose that 2 is treated as a random variable, and the prior distribution for 2 is Gamma, i.c. 1 ~ Gamma(a, B). The prior pdf for 2 is π(λ)- - ga-1e-ßA for 1 > 0. Г(а)
Transcribed Image Text:Suppose we draw an i.i.d. sample X1, ...,X, from a Poisson(1) distribution, where l is a parameter of unknown value. The pdf of the Poisson(1) distribution is f(xi) x;! Suppose that 2 is treated as a random variable, and the prior distribution for 2 is Gamma, i.c. 1 ~ Gamma(a, B). The prior pdf for 2 is π(λ)- - ga-1e-ßA for 1 > 0. Г(а)
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