Example : Central State University administers computer competency examinations every year. These exams allow students to test out of the introductory computer class held at the university. Results of the exams can be placed in one of the following four states:

State 1: pass all of the computer exams and be exempt from the course

State 2: do not pass all of the computer exams on the third attempt and be required to take the course

State 3: fail the computer exams on the first attempt

State 4: fail the computer exams on the second attempt

The course coordinator for the exams has noticed the following matrix of transition probabilities:

Currently, there are 200 students who did not pass all of the exams on the first attempt. In addition, there are 50 students who did not pass on the second attempt. In the long run, how many students will be exempted from the course by passing the exams? How many of the 250 students will be required to take the computer course?

14-17 A study of accounts receivable at the A&W Department Store indicates that bills are current, 1 month

overdue, 2 months overdue, written off as bad debts, or paid in full. Of those that are current, 80% are paid

that month, and the rest become 1 month overdue. Of the 1 month-overdue bills, 90% are paid, and the rest

become 2 months overdue. Those that are 2 months overdue will either be paid (85%) or be listed as bad

debts. If the sales each month average $150,000, determine how much the company expects to receive

of this amount. How much will become bad debts?

Paid Bad debt current 1 month 2 months

Paid 1 0 0 0 0

Bad debt 0 1 0 0 0

P= current 0.8 0 0 0.2 0

1 month 0.9 0 0 0 0.1

2 months 0.85 0.15 0 0 0

F=establish, & A???

I=

B=

A=

This means that 99.7% of the current bills will be paid, and 0.3% of these will be bad debts.

Thus, 0.997(150,000) = $149,550 will be paid, and

0.003(150,000) = $450 will eventually become a bad debt.