Given an infinite population whose distribution is given by

list the 25 possible samples of size 2 and use this list to construct the distribution of \(\bar{X}\) for random samples of size 2 from the given population. Verify that the mean and the variance of this sampling distribution are identical with the corresponding values expected according to Theorem 6.1.

x f(x) 12345 0.20 0.20 0.20 0.20 0.20