2.2. Let Y₁, Y₂,..., Yn denote a random sample from a gamma distribution with each Y~gamma (0; B) with ß known. Find a sufficient statistic for 0. 2.3. Let X₁, X2,..., Xn denote a random sample with size n from an exponential density with mean 0₁. Find the MLE for 0₁. 2.4. Refer back to Question 2.3. Let X₁, X2, ..., Xn denote a random sample with size n from the exponential density with mean 0₁, and Y₁, Y₂, ..., Yn denote a random sample with size m from the exponential density with mean 1. Find the likelihood ratio test for testing Ho: 0₁ = 1 against Ha: 0₁ # 1.
2.2. Let Y₁, Y₂,..., Yn denote a random sample from a gamma distribution with each Y~gamma (0; B) with ß known. Find a sufficient statistic for 0. 2.3. Let X₁, X2,..., Xn denote a random sample with size n from an exponential density with mean 0₁. Find the MLE for 0₁. 2.4. Refer back to Question 2.3. Let X₁, X2, ..., Xn denote a random sample with size n from the exponential density with mean 0₁, and Y₁, Y₂, ..., Yn denote a random sample with size m from the exponential density with mean 1. Find the likelihood ratio test for testing Ho: 0₁ = 1 against Ha: 0₁ # 1.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please solve only 2.3 and 2.4
Transcribed Image Text:Suppose that Y₁, Y2, ..., Yn constitute a random sample from the density function
1 ₂-y/(0+a),
e
f(y10)
= 0 + a
y > 0,0> -1
elsewhere.
0,
Transcribed Image Text:2.2. Let Y₁, Y₂, ..., Yn denote a random sample from a gamma distribution with each Y₁~gamma(0; B)
with ß known. Find a sufficient statistic for 0.
2.3. Let X₁, X2, ..., Xn denote a random sample with size n from an exponential density with mean
0₁. Find the MLE for 0₁.
2.4. Refer back to Question 2.3. Let X₁, X₂, ..., Xn denote a random sample with size n from the
exponential density with mean 0₁, and Y₁, Y2, ..., Yn denote a random sample with size m from the
exponential density with mean 1. Find the likelihood ratio test for testing Ho: 0₁ = 1 against
Ha: 0₁ # 1.
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