Consider a population of size four, the members of which have values x1, x2, x3, x4....

Consider a population of size four, the members of which have values x₁, x₂, x₃, x₄.

a. If simple random sampling were used, how many samples of size two are there?

b. Suppose that rather than simple random sampling, the following sampling scheme is used. The possible samples of size two are

and the sampling is done in such away that each of these four possible samples is equally likely. Is the sample mean unbiased?