Stochastic

33 312 a worker has a number of machines to repair

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Unformatted text preview: . In front of terminal C at the Chicago airport is an area where hotel shuttle vans park. Customers arrive at times of a Poisson process with rate 10 per hour looking for transportation to the Hilton hotel nearby. When 7 people are in the van it leaves for the 36-minute round trip to the hotel. Customers who arrive while the van is gone go to some other hotel instead. (a) What fraction of the customers actually go to the Hilton? (b) What is the average amount of time that a person who actually goes to the Hilton ends up waiting in the van? 3.6. Three children take turns shooting a ball at a basket. They each shoot until they misses and then it is next child’s turn. Suppose that child i makes a basket with probability pi and that successive trials are independent. (a) Determine the proportion of time in the long run that each child shoots. (b) Find the answer when p1 = 2/3, p2 = 3/4, p3 = 4/5. 3.7. A policeman cruises (on average) approximately 10 minutes before stopping a car for speeding. 90% of the cars stopped are given speeding tickets with an $80 fine. I...
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