A student receiving texts can be modeled as a Poisson process at a rate of 3 per hour.
a) What is the probability that the student receives 2 or more texts in the next 30 minutes?
b) Given that the student received 3 texts in the last 10 minutes, what is the probability that the next text will arrive within 15 minutes?
c) Among a group of 10 students, what is the probability that at least 2 will receive at least one text within 15 minutes?
A student receiving texts can be modeled as a Poisson process at a rate of 3...
The arrival of customers to a store is modeled as a poisson process with an intensity of 12 customers / hour. a) Assume that there have been 4 customers in 15 minutes. Calculate the probability that at least two customers arrived in the first 10 minutes. b) Suppose the store is open for 10 hours a day. Approximately determine the probability that at least 100 customers arrived during this day.
Warnings of a possible virus attack on a particular laptop can be modeled as a Poisson process with 1 warning per hour. a) A person received 3 warnings in the last 1 hour of which 1 warning was 15 minutes back. What is the probability that this person has to wait for more than 3 hours for his next warning? b) In a 3-hour software update going on a laptop of 200 people, what is the probability that less than...
suppose that visits to a website can be modeled by a Poisson process with a rate λ=10 per hour (a) What is the probability that there are more than or equal to 2 visits within a given 1/2 hour interval (b) A supervisor starts to monitor the website from the start of a new shift. then what is the expected value of time waited by the supervisor until the 10th visit to the website during that shift? Suppose that visits...
8. Assume that the number of student complaints that arrive at dean's office can be modeled as a Poisson random variable. Also assume that on the average there are 5 calls per hour. a) What is the probability that there are exactly 8 complaints in one hour? b) What is the probability that there are 3 or fewer complaints in one hour? c) What is the probability that there are exactly 12 complaints in two hours? d) What is the...
8. Assume that the number of student complaints that arrive at dean's office can be modeled as a Poisson random variable. Also assume that on the average there are 5 calls per hour. a) What is the probability that there are exactly 8 complaints in one hour? b) What is the probability that there are 3 or fewer complaints in one hour? c) What is the probability that there are exactly 12 complaints in two hours? d) What is the...
question b The arrival of trucks at a receiving dock is a Poisson process with a mean arrival rate of 2 per hour. a. Find the probability that exactly 5 trucks arrive in a two-hour period. b. Knowing that there were 5 trucks arrived during the first two-hour period, find the probability that exactly 5 trucks will arrive in the next two-hour period.
Trucks arrive at a loading/unloading station according to a Poisson process with a rate of 2 trucks per hour. Determine the probability that at least 3 trucks will arrive at the station in the next 30 minutes, A. 0.86 B. 0.59 C. 0.13 D. 0.81 E. 0.08
5. Students arrive at a cafeteria according to a Poisson process at a rate of 20 students per hour. With probability of 0.8, a student will dine in (rather than making a to go order) (a) What is the expected number of students to arrive at a cafeteria in 1 hour? (b) What is the expected number of students to arrive at a cafeteria in a 5 hour period? What assumption did you make? (c) What is the probability that...
2. (15) The time when goals are scored in footbal game are modeled as a Poisson process. such a process, assume that the average time between goals is 30 minutes. For a) (5) Find the probability that at least two goals are scored in the first 30 minutes. (5) In a 90-minute game, find the probability that a fourth goal is scored in the last 10 minutes b) c) (5) Find the expected number of goals in the first 45...
Problem 2. Customers arrive at a call center according to a Poisson process with rate 6/. (a) Find the probability that the 5th call comes within 10 minutes of the 4th call. (b) Find the probability that the 9th call comes within 15 minutes of the 7th call.