51. A new Oxbridge professor wishes to buy a house, and can afford to spend up to one million pounds.Declining the services of conventional estate agents, she consults her favourite internet property pageon which houses are announced at the times of a Poisson process with intensity λ per day. Houseprices may be assumed to be independent random variables which are uniformly distributed over theinterval (800,000, 2,000,000). She decides to view every affordable property announced during thenext 30 days. The time spent viewing any given property is uniformly distributed over the range (1, 2)hours. What is the moment generating function of the total time spent viewing houses?

Answered: Image /qna-images/answer/86775f6d-b887-4768-a417-780567f55a01.jpg

Answered: 51. A new Oxbridge professor wishes to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You are a birdwatcher listening for bird calls in a quiet park on a peaceful April day.Based on your experience, you hear an average of one bird call per minute. Also, when youhear a bird call, it’s a robin 12of the time, a woodpecker 13of the time, and a sparrow 16ofthe time.Assuming that three types of bird calls are independent Poisson processes, identify the distributions of the following random variables: give the name of the distribution and its parameters.(a) W is the time it takes you to hear a woodpecker call.(b) R is the number of robin calls you hear over the course of an hour.(c) T is the time it takes you to hear 10 bird calls total.(d) After you’ve heard 10 bird calls total, S is the number of sparrow calls you’ve heard.
Watershed is a media services company that provides online streaming movie and television content. As a result of the competitive market of streaming service providers, Watershed is interested in proactively identifying will unsubscribe in the next three months based on the customer's characteristics. For a test set of customers, the file Watershed contains an indication of whether a customer unsubscribed in the past three months and the classification model's estimated unsubscribe probability for the customer. In an effort to prevent customer churn, Watershed wishes to offer promotions to customers who may unsubscribe. It costs Watershed $15 to offer a promotion to a customer. If offered a promotion, it successfully persuades a customer to remain a Watershed customer with probability 0.7, and the retaining the customer is worth $60 to Watershed. Click on the datafile logo to reference the data. Assuming customers will be offered the promotion in order of decreasing estimated…
Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 20 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 25 customers per hour. The manager’s service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 33 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations.Wq = 2.797 minutes Hire a second person to…
A barbershop is operated by one barber and has a space capacity to accommodate for a total of 6 customers (including the one in service). If a customer comes to this shop and finds it full, he goes to other shops. Customers arrive according to Poisson distribution at a rate of 4.1 customers per hour. The barber’s service time is exponential and he can serve at a rate of 7.1 customers per hour. a. What is the probability that the barber is free? Answer = Answer b. What is the expected number of people in the system? Answer = Answer c. What is the expected waiting time in the queue? Answer = Answerhours. (hint: use effective arrival rate)
10) The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 9.3 tickets per day. Find the probability that exactly four tickets are written on a randomly selected day from this distribution.
A new phone-answering system installed by a certain utility company is capable of handling ten calls every 5 minutes. Prior to installing the new system, company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to four every 5 minutes. If the analysts are correct about this incoming call distribution, what is the probability that in a 5-minute period more calls will arrive than the system can handle? Based on this probability, comment on the adequacy of the new answering system. The probability that more calls will arrive than the system can handle is

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