Let Y₁, Y₂, Y₃, and Y₄ be independent, identically distributed random variables from a population with mean m and variance s².

Let

denote the average of these four random variables.

(i) What are the expected value and variance of Y̅ in terms of m and s²?

(ii) Now, consider a different estimator of µ:

This is an example of a weighted average of the Yi. Show that W is also an unbiased estimator of µ. Find the variance of W.

(iii) Based on your answers to parts (i) and (ii), which estimator of m do you prefer, Y̅ or W?

Transcribed Image Text:

Y = -(Y, + Y, + Y, + Y,)