Question

Consider the following estimator of the sample mean, µx:                         Z = x1/3 + 2x2­/5 +...

  1. Consider the following estimator of the sample mean, µx:

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

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

            Did you need to make any assumptions?

  1. Assume µx = σx2 = 1 and n = 3. Which estimator, Z or x, has the lower Mean Squared Error?
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