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Suppose that we have data y = (v1.....yn). Each data-point y, is assumed to be generated by a distribution with the following probability density function: Pyin) knye, y ≥ 0. The unknown parameter is ŋ, with x assumed to be known, and 77, K > 0. (a) Write down the likelihood for n given y. Find an expression for the maximum likelihood estimate (MLE) ). (b) A Gamma(a, 3) distribution is chosen as the prior distribution for n. Show that the posterior distribution is also a gamma distribution with parameters that you should determine.

Suppose that we have data y = (v1.....yn). Each data-point y, is assumed to be generated by a distribution with the following probability density function: Pyin) knye, y ≥ 0. The unknown parameter is ŋ, with x assumed to be known, and 77, K > 0. (a) Write down the likelihood for n given y. Find an expression for the maximum likelihood estimate (MLE) ). (b) A Gamma(a, 3) distribution is chosen as the prior distribution for n. Show that the posterior distribution is also a gamma distribution with parameters that you should determine.

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 that we have data y = (y1,..., yn). Each data-point y; is assumed to be generated by a distribution with the following probability density function: P(v₁|n) = kny¹e, y₁ ≥ 0. The unknown parameter is ŋ, with x assumed to be known, and ŋ,<> 0. (a) Write down the likelihood for n given y. Find an expression for the maximum likelihood estimate (MLE) . (b) A Gamma (a,ß) distribution is chosen as the prior distribution for n. Show that the posterior distribution is also a gamma distribution with parameters that you should determine.
Transcribed Image Text:Suppose that we have data y = (y1,..., yn). Each data-point y; is assumed to be generated by a distribution with the following probability density function: P(v₁|n) = kny¹e, y₁ ≥ 0. The unknown parameter is ŋ, with x assumed to be known, and ŋ,<> 0. (a) Write down the likelihood for n given y. Find an expression for the maximum likelihood estimate (MLE) . (b) A Gamma (a,ß) distribution is chosen as the prior distribution for n. Show that the posterior distribution is also a gamma distribution with parameters that you should determine.
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