I would really appreciate some help!
Suppose that a certain drug is to be administered to two different types of patients A & B. It is known that the mean response of patient of type A is the same as the mean response of patients of type B, but the common value Q of this mean is unknown and must be estimated.
It is also known that the variance of the response of patients of type A is four times as large as variance of the response of patients of type B.
Let X1...Xm be responses of random sample of m patients of type A.
Let Y1...Yn be responses of random sample of n patients of type B.
Estimator Qhat = aX(bar-m_ + (1-a)Y(bar-n)
a) For what values of a, m, and n is Qhat an unbiased estimator of Q?
b) For fixed values of m and n, what value of a yields an unbiased estimator with minimum variance?
Thank you (sorry the question is so long).