A bowl contains 6 chips numbered from 1 to 6. One chip is selected at random and then a second is selected (random sampling without replacement). Let X1 and X2 be the first and second numbers drawn.
(a) Tabulate the joint probability function of X1 and X2.
(b) Tabulate the (marginal) probability functions of X1 and X2.
(c) Are XI and X2 independent?
(d) What is the covariance of X1 and X2?
(e) Find the mean and variance of X1 and X2.
(f) Find the mean and variance of S = X1 + X2 in two different ways.