Suppose that a certain drug is to be administered to two different types of animals A and B. It is known that the mean response of animals of type A is the same as the mean response of animals of type B, but the common value θ of this mean is unknown and must be estimated. It is also known that the variance of the response of animals of type A is four times as large as the variance of the response of animals of type B. Let X1, . . . , Xm denote the responses of a random sample of m animals of type A, and let Y1, . . . , Yn denote the responses of an independent random sample of n animals of type B. Finally, consider the estimator

a. For what values of α, m, and n is an unbiased estimator of θ?
b. For fixed values of m and n, what value of α yield an unbiased estimator with minimum variance?

Transcribed Image Text:

ê = aXm + (1- a)Y.