1. Suppose that and are estimations of the parameter theta. We know that E =theta, E =theta/2, v
=10 and V =4. Which estimator is "better"? In what sense is better? Suppose that and are
estimators of theta. We know that E =theta, E theta, V =12, V =10 and E =6.Compare these
three estimators. which do you prefer? why? Let three random samples of sizes n1=10,n2=8,
and n3=6 be taken from a population with mean mu and variance sigma2. Let and be the
sample variances. show that
Solution
3 is preferred because it has the least variance
V( 3) =6 - [E( 3)]^2 , which is less then 10 or 6.