Please verify if my solution to the statistics problemis correct. Are the Method of the Moments (MOM) and the Maximum Likelihood Estimators (MLE) correct?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Please verify if my solution to the statistics problemis correct. Are the Method of the Moments (MOM) and the Maximum Likelihood Estimators (MLE) correct? 

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Step 1

The method of moments estimators are obtained by equating sample moments and population moments, which has been done correctly in parts (a), (b) in above given solution.

There is one minute mistake (although the final answer will be unaltered) in part (c) calculation of MOM estimator in the line where integration by parts has been used, and the following line should have been used :

Statistics homework question answer, step 1, image 1

 

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