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ex_6 - Spring 2009 OR3510/5510 Problem Set 6 In view of the...

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Spring 2009 OR3510/5510 Problem Set 6 In view of the coming break, this is due March 23 on the first Monday after break. Reading: We have finished our work on the Poisson process and variants in Chapter 5 and are now in continuous time Markov chains in Section 6. x/y=page x, problem y in Ross. (1) 352/43 (2) 354/49 (3) Traffic on Snyder Hill Road follows a Poisson process with rate 2/3’s of a vehicle per minute. 10% of the vehicles are trucks and the other 90% are cars. (a) What is the probability at least one truck passes in an hour? (b) Given that 10 trucks have passed by in an hour, what is the expected number of vehicles that have passed by? (c) Given 50 vehicles have passed by in an hour, what is the probability there were exactly 5 trucks and 45 cars. (4) Harry combats drug usage: Incidents of drug usage go on in the bathroom of Harry’s Restaurant. The times of these incidents constitute a Poisson Process of rate 2 per hour. Harry is concerned about this because of the possible effect on business and because he worries about how effective the government’s war on drugs will be. Consequently, Harry
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