For a random sample of size n from a population of size N, consider the following as an...

For a random sample of size n from a population of size N, consider the following as an estimate of μ:

a. Find a condition on the ci such that the estimate is unbiased.

b. Show that the choice of c_i that minimizes the variances of the estimate subject to this condition is c= = 1/n, where i = 1, . . . , n.