2.1. Refer to Question 1.5.2.1.1. Is the MLE consistent?2.1.2. Is the MLE an efficient estimator for 0.2.2. Let Y₁, Y₂, ..., Yn denote a random sample from a gamma distribution with each Y₁~gamma(0; p)with 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 mean0₁. 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 theexponential density with mean 0₁, and Y₁, Y₂, ..., Yn denote a random sample with size m from theexponential density with mean 1. Find the likelihood ratio test for testing Ho: 0₁ = 1 againstHa: 0₁ # 1.2.5. Use the likelihood ratio test to test Ho: 0₁ = 1 against Ha: 0₁1 with a ≈ 0.01 when X = 2and n = 50. 1.5. Suppose that Y₁, Y₂, ..., Yn constitute a random sample from the density function1-e-y/(0+a)f(yle) = 0 + a0,y> 0,0> -1elsewhere.1.5.1. Find the method of moments estimator and the variance of this estimator.1.5.2. Find the maximum likelihood estimator (MLE) for and determine if the MLE isunbiased or not.

As per bartleby guidelines we can solve only first question including three subparts and rest can be…

Answered: 1.5.1. Find the method of moments…

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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1.5.1. Find the method of moments estimator and the variance of this estimator. 1.5.2. Find the maximum likelihood estimator (MLE) for and determine if the MLE is unbiased or not.