Cars arrive at a highway rest area according to a Poisson process with rate 9 per...
A car wash has one automatic car wash machine. Cars arrive according to a Poisson process at an average rate of 5 every 30 minutes. The car wash machine can serve customers according to a Poisson distribution with a mean of 0.25 cars per minute. What is the probability that there is no car waiting to be served?
7.1. Cars arrive to a toll booth 24 hours per day according to a Poisson process with a mean rate of 15 per hour. (a) What is the expected number of cars that will arrive to the booth between 1:00 p.m. and 1:30 p.m.? (b) What is the expected length of time between two consecutively arriving cars! (c) It is now 1:12 p.m. and a car has just arrived. What is the expected number of cars that will arrive between...
On a highway, cars pass according to a Poisson process with rate 5 per minute. Trucks pass according to a Poisson process with rate 3 per minute. The two processes are independent. Let Nc(t) and NT(t) denote the number of cars and trucks that pass in t minutes, respectively. Then N(1)=NC(1)+NT(1) is the number of vehicles that pass in minutes. Find P(NT(3)-71N(3)-20)ยท f) Find E(N(4)INT(3)-7). Hint: NT(4)={NT(4)-NT(3)}+NT(3).
This problem is based on poisson process Cars arrive at a rate alpha-500/HOUR A pedestrian arrives at a crossing point right after the event of a car passing by. If the pedestrian needs 5 seconds to cross the street, what is the probability that he/she will cross safely without getting hit by a car?
Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10messages per hour. a) What is the probability that hte first message arrives in the first 5 minutes? (randome variable time) b) What is the probability that 3 messages arrive in 20 minutes? (random variable # of messages)
Emails arrive at an average rate of 9 per hour. A. What is the probability that more than 5 emails arrive over the next hour? B. What is the probability that the next email arrives within 5 minutes?
2. Suppose buses arrive at a bus stop according to an approximate Poisson process at a mean rate of 4 per hour (60 minutes). Let Y denote the waiting time in minutes until the first bus arrives. (a) (5 points) What is the probability density function of Y? (b) (5 points) Suppose you arrive at the bus stop. What is the probability that you have to wait less than 5 minutes for the first bus? (c) (5 points) Suppose 10...
race cars arrive to a carwash according to a Poisson distribution with a mean of 5 cars per hour. a. What is the expected number of cars arriving in 2 hours?m b. What is the probability of 6 or less cars arriving in 2 hours? c. What is the probability of 9 or more cars arriving in 2 hours
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...
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