Suppose a bowl has 9 chips; one chip is labeled "1", three chips are labeled "3", and five chips are labeled "5". Suppose two chips are selected at random with replacement. Let the random variable X equal the absolute difference between the two draws (e.g. if the first draw is a 1 (11) and the second draw is a 5 (52), then the absolute difference is 15 = 4).

(a) Find the probability distribution of X.

(b) Find the probability that both draws are the same.

(c) Find the probability that both draws are not the same.

(d) Given that both draws are not the same, determine the probability that the

absolute difference is equal to 2, i.e. find P (X = 2X > 0).

(e) On average, what is X equal to?

4.10 Repeat question 4.9(a) assuming the chips are drawn without replacement.