Suppose that x1 and x2 are random samples of observations from a population with mean m and variance s2 Consider the following three point estimators, X, Y, Z, of m X 1 2 x1 1 2 x2 Y 1 4 x1 3 4 x2 Z 1 3 x1 2 3 x2 a Show that all three estimators are unbiased b Which of the estimators is the most efficient c Find the relative efficiency of X with respect to each of the other two estimators

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Question: Suppose that x1 and x2 are random samples of observations from a population with mean m and variance s2. Consider the following three point estimators,

Suppose that x1 and x2 are random samples of observations from a population with mean m and variance s2. Consider the following three point estimators, X, Y, Z, of m:

X =

1 2

x1 +

1 2

x2 Y =

1 4

x1 +

3 4

x2 Z =

1 3

x1 +

2 3

a. Show that all three estimators are unbiased.

b. Which of the estimators is the most efficient?

c. Find the relative efficiency of X with respect to each of the other two estimators.

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