The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"+ proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number offailures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with μ = 1. (Round your answers to three decimal places.)(a) Obtain P(X ≤5) by using the Cumulative Poisson Probabilities table in the Appendix of Tables.P(X ≤ 5) =(b) Determine P(X = 2) from the pmf formula.P(X= 2) =Determine P(X = 2) from the Cumulative Poisson Probabilities table in the Appendix of Tables.P(X= 2) =(c) Determine P(2 ≤ X ≤ 4).P(2 ≤ x ≤ 4) =(d) What is the probability that X exceeds its mean value by more than one standard deviation?

Poission distribution The Poisson distribution is a discrete probability function that means the…

Answered: The article "Expectation Analysis of…

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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Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 55.0 kg and standard deviation ? = 8.4 kg. Suppose a doe that weighs less than 46 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)(b) If the park has about 2850 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)does(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 52 kg. If the average weight is less than 52 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 40 does is less than…
Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 53.0 kg and standard deviation ? = 8.7 kg. Suppose a doe that weighs less than 44 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)(b) If the park has about 2150 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)____ does(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 80 does should be more than 50 kg. If the average weight is less than 50 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 80 does is less…
Q1. Please answer the question with details.
Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ = 20 (suggested in the article "Dynamic Ride Sharing: Theory and Practice"+). (Round your answer to three decimal places.) (a) What is the probability that the number of drivers will be at most 18? (b) What is the probability that the number of drivers will exceed 29? (c) What is the probability that the number of drivers will be between 18 and 29, inclusive? What is the probability that the number of drivers will be strictly between 18 and 29? (d) What is the probability that the number of drivers will be within 2 standard deviations of the mean value? You may need to use the appropriate table in the Appendix of Tables to answer this question.
Suppose data x is distributed with poisson distribution with λ=100 then find the probability of x=99
Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter = 20 (suggested in the article "Dynamic Ride Sharing: Theory and Practice). (Round your answer to three decimal places.) (a) What is the probability that the number of drivers will be at most 14? 0.039 X (b) What is the probability that the number of drivers will exceed 27? (c) What is the probability that the number of drivers will be between 14 and 27, Inclusive? What is the probability that the number of drivers will be strictly between 14 and 277 (d) What is the probability that the number of drivers will be within 2 standard deviations of the mean value? You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Reed It
The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let β > 0 be a constant. Then y = 1 β e−x/β is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities. If a and b are any numbers such that 0 < a < b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is the following. P(a < x < b) = e−a/β − e−b/β Notice that by definition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are the following. μ = β and σ = β Note: The number e = 2.71828 is used throughout…
A certain brokerage house wants to estimate the mean daily return on a certain stock. A random sample of 12 days yields the following return percentages.−1.81, 1.54, 1.52, −2.58, −2.3, 0.97, 0.93, −1.06, 1.04, 0.2, −0.63, −2.75 Send data to calculator If we assume that the returns are normally distributed, find a 90% confidence interval for the mean daily return on this stock. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: ? Upper limit: ?
(a) On the average, it is known that 6 customers arrive at a restaurant per hour according to a Poisson distribution. Find the probability that 10 customers arrived at the restaurant in the next hour. (i) (ii) (iii) 5 to 7 customers arrived at the restaurant in the next 2 hours. less than I customer arrived at the restaurant in the next 30 minutes. (b) Suppose the probability that there will be no cars arriving at a service centre per hour is 0.20. Determine the expected number of cars that will arrive at the service centre in the next hour.
What do i specifically put in the box as p(x)=
(c) Does this Poisson distribution provide a good model for the number of accidents in this example (as per Table 1)? Explain why or why not. Use R to produce a graph to help support your answer (produce the R as part of your answer). (d) Use the model in (b) to estimate the probability that less than 2 accidents were recorded in any randomly chosen week. How does this compare to the actual data?

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