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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(y₁|0)== - 1/7 exp(-2) ₁ 31₁ 2 0. The unknown parameter is 0, with > 0. (a) Write down the likelihood for @ given y. Find an expression for the maximum likelihood estimate (MLE) 8. (b) A Gamma(a,ß) distribution is chosen as the prior distribution for 8. Derive the resulting posterior distribution for given y.

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(y₁|0)== - 1/7 exp(-2) ₁ 31₁ 2 0. The unknown parameter is 0, with > 0. (a) Write down the likelihood for @ given y. Find an expression for the maximum likelihood estimate (MLE) 8. (b) A Gamma(a,ß) distribution is chosen as the prior distribution for 8. Derive the resulting posterior distribution for given y.

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: 8² p(y; | 0) = = = = exp( - ), y₁ ≥ 0. The unknown parameter is 0, with 0 > 0. (a) Write down the likelihood for given y. Find an expression for the maximum likelihood estimate (MLE) 8. (b) A Gamma(a,ß) distribution is chosen as the prior distribution for 8. Derive the resulting posterior distribution for 8 given y.
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: 8² p(y; | 0) = = = = exp( - ), y₁ ≥ 0. The unknown parameter is 0, with 0 > 0. (a) Write down the likelihood for given y. Find an expression for the maximum likelihood estimate (MLE) 8. (b) A Gamma(a,ß) distribution is chosen as the prior distribution for 8. Derive the resulting posterior distribution for 8 given y.
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