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Suppose a car rental agency in large city has three locations: a downtown location (labeled A), an airport location (labeled B), and a hotel lecation (labeled C). The agency has a group of delivery drivers to serve all three locations. Of the calls to the downtown location, 30%are delivered in the downtown area, 30% are delivered to the airport, and 40% are delivered to the hotel. Of the calls to the airport location, 40% are delivered in the downtown area, 40% are delivered to the airport, and 20% are delivered to the hotel. Of the calls to the hotel location, 50% are delivered in the downtown area, 30% are delivered to the airport area, and 20% are delivered to the hotel area. After making a delivery, a driver goes to the nearest location to make the next delivery. This way, the location of a specific driver is determined only by his or her previous location. (A) Give the transition matrix. (B) Find the probability that a driver who begins in the downtown location will be at the hotel after two deliveries. (C) In the long run, what fraction of the total number of stops does a driver make at each of the three locations?
What examples (professional, personal, social) can you provide on when we might use each type. What would be the appropriate hypotheses statements for each example
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