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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Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y1, . . ., Yn. Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter μ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. Derive (a) the joint density function f(y;µ) specifying the model. (b) the…
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 principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 19.1% daily failure rate. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?
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Occurrences of landfalling hurricanes during an El Niño event are modeled asa Poisson process in Bove et al. (1998). The authors assert that “During an ElNiño year, the probability of two or more hurricanes making landfall in theUnited States is 28%.” Find the rate of the Poisson process.
The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3 accidents per year. Find the probability that less than three months elapse between accidents.
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Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y₁, . . ., Yn . Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter µ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. (a) Form the maximum likelihood estimate μ^(y) in the model for the parameter μ…
A computer bulletin receives 20 messages per minute which can be modelled as a Poisson Random Process. Suppose that a new computer bulletin was created to control the flow of message. The senders choose this new computer bulletin 30% of the time.Now, what is the new average time it takes for a message to be sent in the first computer bulletin?
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