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ex-7 - Spring 2011 OR3510/5510 Problem Set 7 When this is...

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Spring 2011 OR3510/5510 Problem Set 7 When this is due–break in the usual routine: Because of the coming spring break, this problem set is due Tuesday March 29. The recitation on Monday is converted to an office hour; it will be held in the usual recitation room. Recitations Tuesday-Friday of the week of March 28 will be held as normal and those enrolled for Monday recitation may feel free to attend a recitation later in the week. Reading: We are working on the Poisson process and variants in Chapter 5 and will finish Chapter 5 during the week of March 14.. (1) Happy Harry’s restaurant is well known for serving great food, but it is filthy as hell and hence not for those with weak stomachs. During rush hour, customers arrive at Happy Harry’s according to a Poisson process of rate a . Customers peek in the door and with probability q they decide the filth is not for them and depart; with probability p they enter and eat. What is the distribution of the waiting times between entrances of customers into the restaurant? What is the mean and variance of this waiting time?

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