Answer Happy

1. Consider a random variable W with unknown population mean y. We have four estimators for y. They are 1, 7, ji and . The estimators have the following distributions: > N(21, vº), Ã N(1, 2), 1 x N(1,0°), i 2. For ī, the above distribution of N(2,0%) indicates that E() = 2 and Var(A) = o2: the other estimators' mean and variance are defined in the same fashion. (a) (10 points) Is there an unbiased estimator of p in the above? Find all unbiased estimators and explain what it means for an estimator to be unbiased. (b) (10 points) Find the most efficient estimator out of the four estimators. You must explain for full credit. (c) (10 points) Suppose we want to pick one estimator between i and it. It is known that 1 = 4 and o = 3, which estimator would you choose using the mean squared error criterion? Show your work.