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Let X₁, ..., X be a random sample from a gamma distribution with a x = 2 and 3 = = 0. '1' 1. Find the simplified likelihood of 0 given x: L(01x). 2. Find the maximum likelihood estimator of 0,0 MLE* is unbiased. 3. Show that the value you found for 0 MLE

Let X₁, ..., X be a random sample from a gamma distribution with a x = 2 and 3 = = 0. '1' 1. Find the simplified likelihood of 0 given x: L(01x). 2. Find the maximum likelihood estimator of 0,0 MLE* is unbiased. 3. Show that the value you found for 0 MLE

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
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**Gamma Distribution Estimation** Let \( X_1, \ldots, X_n \) be a random sample from a gamma distribution with parameters \( \alpha = 2 \) and \( \beta = \theta \). 1. **Likelihood Function**: Find the simplified likelihood of \( \theta \) given \( x \): \( L(\theta | x) \). 2. **Maximum Likelihood Estimator**: Find the maximum likelihood estimator of \( \theta \), denoted as \( \hat{\theta}_{MLE} \). 3. **Unbiased Estimator**: Show that the value you found for \( \hat{\theta}_{MLE} \) is unbiased.
Transcribed Image Text:**Gamma Distribution Estimation** Let \( X_1, \ldots, X_n \) be a random sample from a gamma distribution with parameters \( \alpha = 2 \) and \( \beta = \theta \). 1. **Likelihood Function**: Find the simplified likelihood of \( \theta \) given \( x \): \( L(\theta | x) \). 2. **Maximum Likelihood Estimator**: Find the maximum likelihood estimator of \( \theta \), denoted as \( \hat{\theta}_{MLE} \). 3. **Unbiased Estimator**: Show that the value you found for \( \hat{\theta}_{MLE} \) is unbiased.
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Xi~Gamma(ɑ=2, β=θ)

 

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