T, and S are the sample mean and sample variance from a population with mean, and variance o. Similarly, X, and Sare the sample mean and sample variance from a sec- ond independent population with mean p, and variance o The sample sizes are, and respectively

(a) Show that X-X, is an unbiased estimator of p-H-

(b) Find the standard error of - How could you estimate the standard error?

(c) Suppose that both populations have the same variance; that isa == Show that (-1)+(-1)] is an unbiased estimator of .