Assume a factory that is open 24 hours a day, 7 days per week. Let it

remove high priority products arrive to this business according to a Poisson process

with a rate of two every five minutes, and that low priority products arrive at the

same business according to a Poisson process with a rate of one every ten minutes.

Furthermore, suppose that high and low priority customers arrive independently

of one another.

(i) Determine the probability that fifteen low priority products and twenty high

priority products arrive between 10 PM and 12 PM tomorrow. Explain in detail why this occurs.

(ii) Determine the expected number of arrivals between 12 AM and 8 AM tomor-

row. Explain in detail why this occurs.

(iii) Starting at 9 AM tomorrow, determine the expected time when the twelfth

products arrives to this business. Explain in detail why this occurs.