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…
The average number of collisions in a week during the summer months at a particular intersection is 2. Assume that the requirements of the Poisson distribution are satisfied. What is the probability that there will be exactly one collision in a week?
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.
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?
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?
A service company receives on average 4 service requests per day. The requests are received randomly according to Poisson process. The company has 2 service engineers and sends one engineer to attend each request. 1 An engineer needs an exponentially distributed service time with the mean of day(s). 2 The company's policy is to have maximum of 2 requests waiting in the queue If this number is reached, all incoming requests are rejected (sent to a competitor). Answer the following questions based on the information provide above: (a) Using the Kendall's notation, indicate what type of queueing system it is: (b) Compute the system state probabilities (provide at least 3 decimals): Po = P1= P2 = P3 = Pa = (c) Compute the expected total number of customer requests (waiting and served) in the system. ELL] = (d) Compute the expected number of accepted requests. Aaccepted = (e) Compute the expected total processing time (waiting + being served) for the accepted requests. E[Time] =
1. Provide the graphs for PDF and CDF of the random variable B which takes on values of 1 and 0 with probability of 0.40 and 0.60. (Don't forget the horizontal axis must be sorted).

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