A computer system for modelling air traffic flow of a hub airport that flights arerouted though assumes that fights pass through the hub airport according to aPoisson process with rate A = 20 per hour and that jumbo passenger jets (JPJs)pass through according to an independent Poisson process with rate App per hour.According to the model, we have the following probabilities;• The probability that exactly 2 JPJs and 18 flights pass through the hubairport in one hour is 0.0189.The probability that exactly 4 JPJs and 22 flights pass through the hubairport in one hour is 0.0129.By taking a ratio of these probabilities, or otherwise, use this information tocalculate XjPj

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Answered: A computer system for modelling air…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In England, the most serious emergency calls requesting an ambulance are classified as 'Red 1'. According to data from NHS England, in March 2017, the London Ambulance Service (LAS) received a total of 1597 Red 1 emergency calls. Based on this number and adjusting for variations during the day, suppose that Red 1 calls arriving at the LAS in daylight hours may be modelled as a Poisson process with rate 3 per hour. (i1 (2) Calculate and report the probability that three Red 1 calls arrive at the LAS in 30 minutes during daylight hours. (ii) (1) Write down the distribution of the waiting time (in hours) between the arrivals of two successive Red 1 calls at the LAS during daylight hours, including the values of any parameters. (2) Calculate and report the probability that the gap between the arrivals of two successive Red 1 calls at the LAS during daylight hours will exceed 20 minutes.
The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3.5 accidents per year. Find the probability that more than one year elapses between accidents.
Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 112 homicides. After finding the mean number of homicides per city-year, find the probability that a randomly selected city-year has the following numbers of homicides, then compare the actual results to those expected by using the Poisson probabilities: Homicides each city-year а. О b. 1 с. 2 d. 3 е. 4 Actual results 187 76 15 2
Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 153 homicides. After finding the mean number of homicides per city-year, find the probability that a randomly selected city-year has the following numbers of homicides, then compare the actual results to those expected by using the Poisson probabilities: Homicides each city-year а. О b. 1 с. 2 d. 3 е. 4 Actual results 162 89 24 4 1 a. P(0) = (Round to four decimal places as needed.) b. P(1) =D (Round to four decimal places as needed.) c. P(2) = (Round to four decimal places as needed.) d. P(3) = (Round to four decimal places as needed.) e. P(4) = (Round to four decimal places as needed.) The actual results consisted of 162 city-years with 0 homicides; 89 city-years with one homicide; 24 city-years with two homicides; 4 city-years with three homicides; 1 city-year with four homicides. Compare the actual results to those expected by using the Poisson probabilities. Does the Poisson…
Chains "A" and "B" are made of the same steel. "A" consists of three links and "B" consists of six links, each link having a normal distribution function of the resisting strength with a mean of 60,000 psi and standard deviation of 5,000 psi. Determine which chain is generally weaker (from a probabilistic point of view) by plotting the probability distribution functions of their resisting strengths on the same diagram.
Assume that arrivals of cars at a gas station can be modeled by a Poisson process with rate 2 cars per hour. What is the probability that one has to wait at least 3 hours for the arrival of 3 cars?

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