Answer Happy

1. Consider a random variable W with unknown population mean y. We have four estimators for y. They are î, , j and ii. The estimators have the following distributions: î~ N(24,0%), Ñ ~ N(4,20), i ~ N(4,02), i~ N(V,0.10). where o > 2. For ī, the above distribution of N (24, 02) indicates that E(A) = 211 and Var(î) = o2: the other estimators' mean and variance are defined in the same fashion. (a) (10 points) Is there an unbiased estimator of je 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 û and it. It is known that H = 4 and o = 3, which estimator would you choose using the mean squared error criterion? Show your work. 2. (5 points) Let Z be the standard normal random variable: that is, ZN(0,1). What is the value of P(-1.5