15.3 Exercise 17

A computer store sells Macintosh, HP, and various other IBM compatible personal computers. It has two major sources of customers:

1. Students and faculty from a nearby university
2. General customers for home and business computing. Suppose the following assumptions are reasonable for monthly purchases.

• The number of university buyers $N 1 \sim$ Poisson (30). The probabilities for Mac, HP, others are 0.4, 0.2, 0.4, respectively.
• The number of non-university buyers $N 2 \sim$ Poisson (65). The respective probabilities for Mac, HP, others are 0.2, 0.3, 0.5.
• For each group, the composite demand assumptions are reasonable, and the two groups buy independently.

What is the distribution for the number of Mac sales? What is the distribution for the total number of Mac and Dell sales?