A scientific committee of 4 persons is to be randomly selected from a group consisting of 3 biologists, 3 physicists and 4 mathematicians. Let X denote the number of biologists, Y the number of physicists and Z the number of mathematician on the commitee.
Find the joint probability mass function of the random vector (X, Y, Z).
Find Cov(X, Y) and Corr(X, Y).
Find Var(X + Y) first by computing the probability mass function of X + Y and then by using your computations in part (a) and the formula for the variance of a sum. Did you get the same answer?