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It has been determined that the service desk in UW's Davis Centre Library receives, on average, 2 visits every 15 minutes. An hour is considered

It has been determined that the service desk in UW's Davis Centre Library receives, on average, 2 visits every 15 minutes. An hour is considered an "unproductive" hour if no one visits the service desk during the hour. When calculating probabilities, assume service desk visits follow a Poisson process. a) Discuss how each of the three assumptions of the Poisson process may be violated in this situation. b) Calculate the probability of an "unproductive" hour. c) Calculate the probability of 25 service desk visits in a 2-hour period. d) Visits to the service desk are for a number of different requests. There is a 10% probability that a visit is for booking a study room. Only one study room can be booked per visit. If, on a given day, it took 10 service desk visits for the first 3 study rooms to be booked, calculate the probability that 2 study rooms were booked in the first 4 visits.

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