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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A database server is designed to handle a maximum of 100 transactions per second. If transactions arrive at the rate of 75 per second, what is the probability that the server is overloaded? You may assume that arrivals follow a Poisson distribution.
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.
A believer in the "random walk" theory of stock markets thinks the value of an index of stock prices has a 0.6 probability of rising in any year. The change in the value of the index in any given year is not affected by whether it rose or fell in earlier years. You plan to record the value for the index in each of the next eight years. Let the random variable, X, represent the number of years (out of the next 8 years) in which the value of the index rises. a) If X is distributed according to the binomial probability distribution, what are the values for n and p?o b) What are the possible values X can take, or equal? QMETH 201, Homework 3 c) Calculate the probability X = 30 d) Calculate the expected value for X. e) Calculate the standard deviation for X. 4
When three or more orders are placed, one (1) technical expert from PLDT, the country's broadband and digital services provider, is assigned to the city. For a 100,000-person city, supposed orders follow a Poisson distribution with a mean of 0.25 each week. Suppose your city has a population of 800,000 people, and if you are the first one in the city to place an order, what is the probability that you have to wait more than two weeks from the time you place your order until a technician is dispatched? a. 0.3281 b. 0.2381 c. 0.0183 d. 0.0916
Suppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves is less than $28.00, hers would be less likely to sell. Mairin selected a random sample of 9 similar hand‑knit, wool‑blend infinity scarves, and their prices are as follows. $21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00 Use a left‑tailed one‑sample ?t‑test to determine whether the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed. Mairin should (reject, accept, fail to accept) her null hypothesis. There is (sufficient, no, insufficient) evidence that the mean price of hand‑knit, wool‑blend infinity scarves is (greater than, different from, less than, equal two) $28.00.
A traffic enforcer counts the number of vehicle at a specific location in the highway. In his counting, there are 400 vehicles arriving per hour. Assuming that the arrival of vehicles is Poisson distributed, estimate the probabilities of having 0, 1, 2, 3, 4, and 5 or more vehicles arriving over a 20-second time interval.
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 company that bakes chocolate chip cookies averages 5.2 chocolate chips per cookie. Assume that the number of chocolate chips per cookie follows the Poisson distribution. What is the probability that a randomly selected cookie will contain two or more chocolate chips?
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)
Gregory decides to go to this well-known transpo hub on his way home from work so that he can take a taxi or a bus there. Poisson distribution can be used to define the arrival of each of his options. A taxi comes every eight minutes, while a bus comes every ten. While a taxi can accommodate 15 passengers, a bus can accommodate 30. Taxis and buses come separately. 1 . What's the likelihood that five buses will show up within the next hour?2. What's the likelihood that no cab will show up in the ensuing 45 minutes?3 . What's the likelihood that Gregory will be leaving the terminal after 15 minutes if there are 30 persons waiting in front of him?4. What's the likelihood that Jordan will be on his way home after 30 minutes of waiting and the arrival of no more than two cabs, assuming that there are 100 passengers in line ahead of him in the terminal?
A taxi service receives an average of 10.4 calls a day from customers who need a ride to the airport. Use the Poisson distribution to find the probability that exactly 8 customers need a ride on a given day. Do not round intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)
A certain kind of sheet metal has, on average, 4 defects per 20 square feet.Assuming a Poisson distribution, find the probability that a 28 square foot metal sheet has at least 7 defects. Round your answer to three decimal places.

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