Suppose that x1 and x2 are random samples of observations from a
population with mean μ and variance σ2. Consider the following
three point estimators, X, Y, and Z, of μ: X = (-x1 + x2)/2, Y =
(x1 + 3x2)/4, and Z = (x1 + 2x2)/3.
a) Calculate the bias for the estimators. Are any of them
unbiased?
b) Compare the efficiency of these estimators.
c) Which one (if any) would you choose to estimate μ
considering your answers to both a and b?