Suppose that visitors to a state carnival which is open from 5 pm to 10 pm daily arrive according toa non-homogeneous Poisson process. The rate at which visitors arrive decreases linearly from 30 perhour at 5 pm to 5 per hour at 10 pm. What is the probability that 3 customers will arrive between9:30 pm and 10 pm?

Solution: From the given information, arrival of visitors follows a non-homogeneous Poisson process.…

Answered: Suppose that visitors to a state…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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11. If outside line accesses from within a local phone network form a Poisson process with rate 1/ min., find the joint probability that the cumulative number of accesses is equal to 2 at time 1 minute, 3 at time 2 minutes, and 5 at time 3 minutes.
Assume that the number of automobiles arriving at a gasoline station is Poisson distributed and occur at an average rate of 50/hour. The station has only one gasoline pump. If all cars are assumed to require one minute to obtain fuel, what is the probability that a waiting line will occur at the pump?
Q10. Customers arrive in a grocery store according to a Poisson process with rate 6 per hour. What is the probability that exactly one customer has arrived between 9:00 am and 9:20 am? (A) 2e-² (B) 6e-6 (C) 8e-6 (D) 1/3 (E) None of the above
On Monday mornings, the First National Bank only has one teller window open for deposits and withdrawals. Experience has shown that the average number of arriving customers in a four-minute interval on Monday mornings is 1.8, and each teller can serve more than that number efficiently. These random arrivals at this bank on Monday mornings are Poisson distributed. Find the probability that within four minutes interval at least one customer will arrive.
Suppose that customers arrive at a diner at a Poisson rate of A = 3 per hour. What is the probability that exactly 6 customers arrive between 1PM and 3PM and that exactly 4 customers arrive between 4PM and 5PM? Hint: You're dealing with two discrete rv's, in this case. (Answer as a decimal number, and round to 3 decimal places).
Suppose that on the average, 5 customers arrive at a shop during a 1-hour period. Assume arrival times of customers follow a Poisson Process. Find the probability that no customer will arrive within 10 minutes. Find the probability that the fifth customer will arrive after an hour. (Hint: NOT 36.8% and 17.5%)
The arrival of buses from the campus to student housing in the late afternoon is modeled by a Poisson process with an interarrival time of 30 minutes. Consider the situation where a bus has just arrived at 4.29 PM. (a) A student arrives at 4.30 PM and misses the bus. Find the expected value of time that the student will have to wait for the next bus to student housing? (b) At 4.52 PM the next bus has not yet arrived, and another student comes to the bus stop. Find the expected value of time that these two students will have to wait for the next bus?
2. Suppose the defective rate at a particular factory is 1%. Suppose 50 parts were selected from the daily output of parts. Let X denote the number of defective parts in the sample. a) Find the probability that the sample contains exactly 2 defective parts. b) Use Poisson approximation to find the probability that the sample contains exactly 2 defective parts. c) Find the probability that the sample contains at most 1 defective part. d) Use Poisson approximation to find the probability that the sample contains at most 1defective part.
Suppose that arrivals to an emergency room follow a Poisson process with meantwo patients every 5 minutes. Calculate the probabilities of (a) no customers in 2 minutes; (b) exactly 2 customers in a minute; (c) exactly 5 customers in 3 minutes;and (d) no more than 2 customers in 5 minutes.
(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.
The flow of goods through a certain machine in a factory can be modeled as a Poisson Random Process. Suppose that a machine has 20 goods per minute as an outflow rate, determine the probability that the 7th good will exit within 30 seconds. (Express your answer in 4 decimal places)
A manufacturing company claims that the number of machine breakdowns follows a Poisson distribution with a mean of two breakdowns every 500 hours. Let x denote the time (in hours0 between successive breakdowns. assuming that the manufacturing company's claim is true, find the probability that the time between successive breakdowns is at most five hours.

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