Suppose that 40 percent of the students in a large population are freshmen, 30 percent are sophomores, 20 percent are juniors, and 10 percent are seniors. Suppose that 10 students are selected at random from the population, and let X1, X2, X3, X4 denote, respectively, the numbers of freshmen, sophomores, juniors, and seniors that are obtained.
a. Determine ρ(Xi, Xj) for each pair of values i and j (i < j).
b. For what values of i and j (i < j) is ρ(Xi, Xj) most negative?
c. For what values of i and j (i < j) is ρ(Xi, Xj) closest to 0?