11. A Poisson distribution is used to model so-called a Poisson phenomenon. Find out what a Poissonphenomenon is and provide an intuitive logic why sum of two independent Poisson variables is Poisson.12. Do the Taylor series expansion for e" and use it to show E [X] = V [X] = for an X - Poisson (u).13. Think of the following Riemann integral for a contimuous function f:1112

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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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Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.5 per year. Find the probability that, in a year, there will be 4 hurricanes. In a 55-year period, how many years are expected to have 4 hurricanes? How does the result from part (b) compare to a recent period of 55 years in which 8 years had 4 hurricanes? Does the Poisson distribution work well here? (*Please before midnight!)
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What type of distribution is appropriate to model the time between two consecutive departures from the gate of an airport Poisson Binomial Exponential Geometric
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Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. a What percentage of time all dispatchers are idle? b What percentage of time only one dispatcher is busy? c. What is the average number of callers in the system? d What is the average time in minutes that a customer spends in the system? e What is the total cost of the system for 8 hours if each dispatcher charges $25 /hour and the waiting cost per hour for…
Steve Burns, host of the first season of Blue' clues recently bids goodbye to the show. Assuming that in his first season of hosting he can actually find an average of 15 clues that when blue leaves paw prints on the objects around her house per week. If the clues he finds follows Poisson distribution, what is the probability that there will be 5, 10 or 15 clues during the next week?

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A Poisson distribution is used to model so-called a Poisson phenomenon. Find out what a Poisson phenomenon is and provide an intuitive logic why sum of two independent Poisson variahles is Poisson.