(a)On the average, it is known that 6 customers arrive at a restaurant per houraccording to a Poisson distribution. Find the probability that10 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 perhour is 0.20. Determine the expected number of cars that will arrive at the servicecentre in the next hour.

The average number of customers who arrive at a restaurant per hour is 6. Assume λ=6 Poisson…

Answered: (a) On the average, it is known that 6…

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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At a toll-booth on-ramp there is a stochastic arrival distribution. Vehicles are counted in 20-second intervals, and vehicle counts are taken in 120 of these time intervals. Based on data collected, no vehicles arrived in 18 of the 120 count intervals. What is the number of the 120 intervals that 3 cars arrived?
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Consider a Poisson distribution with a mean of two occurrences per time period. Compute the probability of three occurrences in one time period (to 4 decimals). Compute the probability of seven occurrences in two time periods (to 4 decimals).
On average, Nancy has noticed that 21 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 1 truck will pass her apartment in a 2-hour time period using Poisson distribution, find the average number of trucks per 2 hours.
Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y₁, . . ., Yn . Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter µ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. (a) Form the maximum likelihood estimate μ^(y) in the model for the parameter μ…
(b) Suppose the number of customers at a Sushi outlet is Poisson distributed where an average of nineteen customers are served per 30 minutes. (i) Over a fifteen-minute period, how many customers are served on average? Find the probability of exactly seven customers served over a fifteen-minute period. Write your answer correct to 4 decimal places. (iii) Calculate the probability at least 1 customer is served over a fifteen-minute period. Write your answer correct to 4 decimal places.
Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store. If X = the number of arrivals per minute:Find the probability of 8 customers or less arriving within a minute. Find the probability of more than 7 customers arriving within a minute. Find the probability of 3 customers arriving within a minute.
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?
A company advertise their products on Instagram. The number of times their advertise- ments are clicked on follows a Poisson distribution with a rate of 18 clicks per minute.
The number of admissions per day at an emergency room has a Poisson distribution and its parameter is 5.Find the probability of I. At least 3 admissions per day II. At most 8 admissions per day.

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