Introductory Econometrics 4th Edition by Jeffrey Wooldridge

تمرين 4

This is a more general version of Problem
Problem Let Y 1 , Y 2 , Y 3 , and Y 4 be independent, identically distributed random variables from a population with mean and variance 2. Let = (Y 1 +Y 2 + Y 3 + Y 4 ) denote the average of these four random variables.
(i) What are the expected value and variance of in terms of and 2
(ii) Now, consider a different estimator of :
W = Y 1 + Y 2 + Y 3 + Y 4.
This is an example of a weighted average of the Yi. Show that W is also an unbiased estimator of . Find the variance of W.
(iii) Based on your answers to parts (i) and (ii), which estimator of do you prefer, YP or W