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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6. The Hayward campus has become a dangerous place for people on motorized scooters. There are six intersections on the campus loop, independent of one another, for which accidents occur following a Poisson process with different rates, say A₁,..., A6, per week. The Board of Campus Safety is interested in the total number of accidents that occur next semester (sixteen weeks). (a) Using the moment generating function, derive the distribution of the total number of accidents that occur next semester at these intersections combined. Make sure you define all variables used. (b) Suppose, from past experience, it is known that the values of A₁,..., A6 are 0.8, 1.2, 2.9, 0.2, 1.1, and 2.8 respectively. What is the probability that there are between 142 and 146 (inclusively) accidents on the campus loop next semester? (c) What is the expected value and standard deviation for the number of accidents on the campus loop next quarter?
1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month Find the probability of the joint sales team (experienced and junior) completing exactly 2 sales in any given months, assuming the two sales people act independently of each other. 1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given months
A car hire firm has two cars, which it hires out day. The number of demands for a car on each day is distributed as a poisson distribution with mean 1.5. calculate the proportion of days on which (i) neither car is used, (ii) the proportion of days on which some demand is refused.
please show steps neatly with answer.
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
11. The probability that a mouse inoculated with a serum will contract a certain disease is 0.02. Using The Poisson approximation, find the probability taht at most 3 of 30 inoculated mice will contract the disease.
5
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] =
Compute the probability that a Random Walk ever returns to the origin and the expected time to the first return.
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…
Suppose that the number of events in a month can be modeled by a Poisson distribution with λ=2/month. Then, what is the distribution of the number of events in a year? a). Poisson with λ=2.4 b). Poisson with λ=24 c). Poisson with λ=12 d). Poisson with λ=2
a) The number of calls coming per minute into a hotels' reservation center is Poisson rand variable with mean 3. (i) Find the probability that no calls come in a given minute period. (ii) Find the probability that no calls come in a given half a minute period. b) Su

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