PART A:

Consider two alternative estimators of the population mean, computed from random samples of size 4. X= (X1 + X3)/2 and X* = (X1 + 2X2 + 3X3 +2X4)/8

Show which estimator is relatively more efficient.

PART B:

X # = (0.5X1 + 0.5X2)/(N-2) + [(X3 +X4 +...+XN)/(N-3)] is an estimator of the population mean based on random sampling (N > 3).

1. Find the variance of this estimator and then check what happens to the variance as N tends to infinity?

2. Is the estimator consistent? Explain clearly why.