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 finite population consisting of more than two categories.)
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