Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 2

This is a more general version of Problem

Problem Let Y1, Y2, Y3, and Y4 be independent, identically distributed random variables from a population with mean ? and variance ?2. Let = (Y1+Y2 + Y3 + Y4) 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 = Y1+ Y2 + Y3 + Y4.

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?

Step 1 of 3

The following variables are random and independent variables with mean µ and variance s².

(i) The mean or expected value of W can be calculated as follows:

The expected mean of W is equal. However if, then