1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μ and V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean: ˆμ1 = (n...

1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μ
and V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean:
ˆμ1 = (n −3/n) ̄X
ˆμ2 = 0.95 ̄X
(a) Which of the estimators is an unbiased estimator for μ?
(b) Which is the variance of the two estimators?
(c) Given the properties above, which one would you prefer? Is there another property that would
influence your decision? Explain.