1. Consider the following estimator of the sample mean (X): Z = x1/3 + 2x2/5 + x3/6. a. Is Z unbiased? Compute the following: Bias(Z),

1. Consider the following estimator of the sample mean (μX):

Z = x1/3 + 2x2/5 + x3/6.

a. Is Z unbiased? Compute the following: Bias(Z), Var(Z), and MSE(Z).

Did you need to make any assumptions?

b. Assuming μX = σx2 = 1 and n = 3, which estimator, Z or x̅, has the lower Mean Squared Error?