Let X1,...,X, be a random sample of distribution f(r:0) = e--9), 1> 0, 0 elsewhere, where 0 >0. (a) Find the mle of 0.
Let X1,...,X, be a random sample of distribution f(r:0) = e--9), 1> 0, 0 elsewhere, where 0 >0. (a) Find the mle of 0.
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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Can you please help solve the advanced statistics and probability theory question below?
parts (b) only please
how to fi nd the Likelihood Ratio Test (LRT) in terms of mle of θ.?
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![Let \( X_1, \ldots, X_n \) be a random sample of distribution
\[
f(x; \theta) = e^{-(x-\theta)}, x > \theta, 0 \text{ elsewhere},
\]
where \(\theta > 0\).
(a) Find the MLE of \(\theta\).
(b) For testing \( H_0 : \theta = \theta_0 \) vs \( H_1 : \theta > \theta_0 \), find the Likelihood Ratio Test (LRT) in terms of the MLE found in part (a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15feef40-32fb-4401-88ed-794608a5d767%2F3f2eb884-fa2f-4066-99a8-1bb8c09abaea%2Frjs450h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( X_1, \ldots, X_n \) be a random sample of distribution
\[
f(x; \theta) = e^{-(x-\theta)}, x > \theta, 0 \text{ elsewhere},
\]
where \(\theta > 0\).
(a) Find the MLE of \(\theta\).
(b) For testing \( H_0 : \theta = \theta_0 \) vs \( H_1 : \theta > \theta_0 \), find the Likelihood Ratio Test (LRT) in terms of the MLE found in part (a).
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