7. (Sec. 3.6) Consider sending packets of data through the internet, and we have a counter that determinesthe number of missing/corrupted packets. Suppose that number X has a Poisson distribution withparameter 23.=(a) What is the probability that the counter determines that the transmission has exactly one miss-ing/corrupted packet of data?(b) What is the probability that the counter determines that the transmission has at least 3 missing/corrupted packets of data?(c) If two transmissions of data across the internet arthat at least one of them does not contain a missing/corrupted packet?e independently selected, what is the probability

As per the question, X follows poisson distribution with mean 0.23Probability density function of…

Answered: 7. (Sec. 3.6) Consider sending packets…

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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Due to COVID-19, the quantity of local parcel deliveries by ADIX courier service has increased over the months. The company's data analyst claims that the current trend of the number of waiting days for local deliveries follows Poisson distribution 2 days. To verify the claim, he collects new data on the number of local parcel deliveries by the courier for the latest six weeks. The data collected and its associated Poisson probability are shown in Table 3. 1) Based on the new data, will the data distribution be the same as initially claimed by the analyst? 2) In your opinion, does the data provides a good fit to the distribution. Justify your answer.
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.
Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter lamda = 1000. Suppose the damage sizes for separate accidents are i.i.d. (independent identically distributed) r.v.'s having an exponential distribution with a mean of $2500. Each policy involves a deductible of $500. Let N1 be the number of accidents that result in claims, and N2 be the number of accidents that do not result in claims. Answer the following questions 1-5. 1. Are N1, N2 dependent? 2. What is the name of the distributions of N1, N2? Compound Poisson or Marked Poisson? 3. What is the mean and variance of N1? 4. What is the mean and variance of N2? 5. Which of the number is close to the probability that N1 will not be larger than 790? (Hint: to what distribution is the Poisson distribution with a parameter of lamda close for "large" lamda's?
Suppose the numbers of times that vending machine A and vending machine B are out of order in a month follow Poisson distributions with means 1 and 2 respectively. Find the probabilities that (a) both vending machines A and B are out of order for 3 times in a month, (b) exactly one vending machine is out of order once in a month, (c) both vending machines A and B work properly for 2 consecutive months. (Give your answers correct to 3 significant figures.)
3 8 Suppose that the number of customers that arrive at an AT&T wireless store can be modeled by a Poisson Distribution, with a mean of 3 customer arrivals every hour. Suppose that the store manager needs to run out of the store for a period of 10 minutes. (a) Compute the probability that no customers will arrive at the AT&T store in that 10-minute period. (b) Compute the probability that three or more customers arrive in that 10-minute period.
Suppose that earthquakes occur according to a Poisson process with rate λ = 0.2 per day. (a) What is the probability that there will be 2 or fewer earthquakes in April? (b) Starting from now, what is the probability that the second earthquake will occur within a week?
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 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 19? (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 19 and 29, inclusive? What is the probability that the number of drivers will be strictly between 19 and 29? (d) What is the probability that the number of drivers will be within 2 standard deviations of the mean value?
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 15? 0.1572 (b) What is the probability that the number of drivers will exceed 27? 0.8168 X (c) What is the probability that the number of drivers will be between 15 and 27, inclusive? 0.7698 X What is the probability that the number of drivers will be strictly between 15 and 27? 0.8439 X (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.
What type of distribution is appropriate to model the time between two consecutive departures from the gate of an airport Poisson Binomial Exponential Geometric
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 times between arrivals in a queue follow an exponential distribution with a rate of 1. Check the incorrect alternative: a) 50% of arrivals will take place before 1 minute. b) If the times between arrivals are exponentially distributed with a rate equal to 1, then arrivals occur according to a Poisson distribution with an average equal to 1. c) Times between arrivals are independent. d) The variance of the times between arrivals is equal to 1. e) There is an average of one arrival every minute.

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