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 X = 20 per hour and that jumbo passenger jets (JPJs)pass through according to an independent Poisson process with rate λJPJ per hour.Telephone calls arrive at a helpline according to a Poisson process with rate \ = 25calls per hour. Explain why the probability of the following two events:• There are no calls for 10 minutes and there are no calls in a 20 minute period,given that there have been no calls in the first 10 of those minutesare the same and calculate this probability.

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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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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.
A computer system for modelling air traffic flow of a hub airport that flights are routed though assumes that fights pass through the hub airport according to a Poisson 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 hub airport in one hour is 0.0189. The probability that exactly 4 JPJs and 22 flights pass through the hub airport in one hour is 0.0129. By taking a ratio of these probabilities, or otherwise, use this information to calculate XjPj
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