8. A stockroom currently has 30 components of a certain type, of which 8 were provided by supplier 1, 10 by supplier 2, and 12 by supplier 3. Six of these are to be randomly selected for a particular assembly.

Let X  the number of supplier 1 s components selected, Y  the number of supplier 2 s components selected, and p(x, y) denote the joint pmf of X and Y.

a. What is p(3, 2)? [Hint: Each sample of size 6 is equally likely to be selected. Therefore, p(3, 2)

(number of outcomes with X  3 and Y  2)/

(total number of outcomes). Now use the product rule for counting to obtain the numerator and denominator.]

b. Using the logic of part (a), obtain p(x, y). (This can be thought of as a multivariate hypergeometric distribution sampling without replacement from a nite population consisting of more than two categories.)