The values of the response variable of a population are: u1 = 2, u2 = 3, u3 = 4, u4 = 5, u5 = 7, u6 = 9.

(a) Determine the mean and the variance 2 of the population.

(b) Compute the mean and variance of y for a simple random sample of size 4 of this population.

(c) Suppose the population is divided into two strata: stratum 1 contains u1 = 2, u2 = 3, u3 = 4, while stratum 2 contains u4 = 5, u5 = 7, u6 = 9. Determine the average and the empirical variance in each of the two strata.

(d) List all samples of size 4 that can be selected by choosing simple random samples of 2 units in each of the strata. For each global sample of size 4, give the probability that it is selected.