# Math

Starting at time t=0, cars arrive at a car wash according to a Poisson process with rate of λ cars/hour. At any given moment, the car wash is either free or occupied. The car wash is initially free at time t=0. If a car arrives at the car wash when it is free, the car is serviced immediately. Service lasts for 1/4 hours, during which the car wash is occupied. If a car arrives at the car wash when it is occupied, the car is denied service and it leaves the car wash.

Question 1--> Write down the PMF pN(k) of N, the number of cars arriving at the car wash between times 0 and 3, in terms of λ and k.

For k=0,1,…,

Question 2--> Find the probability that a car is accepted for service given that it arrives at time t=1/6. Write down your answer in terms of λ, using the standard notation.

Question 3--> Find the PDF fT2(t) of T2, the time until the second serviced car leaves the car wash.
For t≥0.5,fT2(t) =?

Question 4--> Find the probability that exactly one car is accepted for service between t=0 and t=1.

1. 👍 0
2. 👎 0
3. 👁 382

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Pre Algebra

6. Given the function rule f(x)=x^2-3x+2, what is the output of f(-2)? A. -8 B. 0 C. 4 D. 12 7. Suppose you earn \$15 for each car you wash. Which function describes the relationship between your total earnings E and and the number

asked by Summer on March 21, 2016
2. ### physics

Cars A and B are racing each other along a straight path in following manner: Car A has head start and is a distance dA beyond starting line at t=0. The starting line is at x=o. Car A travels at constant speed vA. Car B starts at

asked by help on September 27, 2009
3. ### Physics

Need Help with physics! Two cars drive on a straight highway. At time t = 0, car 1 passes mile marker 0 traveling due east with a speed of 17.0 m/s. At the same time, car 2 is 1.3 km east of mile marker 0 traveling at 30.0 m/s due

asked by Brandon on October 4, 2012
4. ### physics

a)Two cars are traveling along a straight line in the same direction, the lead car at 24.5m/s and the other car at 29.6m/s. At the moment the cars are 41.6m apart, the lead driver applies the brakes, causing her car to have an

asked by Cat on January 23, 2014
5. ### Statistics (Poisson)

Cars arrive at a toll booth according to a Poisson process with mean 80 cars per hour. How long can the attendant's phone call last if the probability is at least .4 that no cars arrive during the call. The book's answer is 23

asked by Sean on July 19, 2009
1. ### Physics Help

1) two cars start at the same location and accelerate for the same amount of time. if one car has twice the acceleration of the other, how will the final speeds of the cars compare? by how much farther will the faster car

asked by Kayla on September 11, 2014
2. ### algebra 1

A theater group is having a carwash fundraiser.The group can only spend \$34 on soap, which is enough to wash 40 cars. Each car is charged \$5. If c represents the total number of cars washed and p represents the profit, which

3. ### probability

1. Busy people arrive at the park according to a Poisson process with rate λ1=3/hour and stay in the park for exactly 1/6 of an hour. Relaxed people arrive at the park according to a Poisson process with rate λ2=2/hour and stay

asked by Brian on November 27, 2018
4. ### statistic

A new car was put into production. It involved many assembly tasks. Each car was inspected at the end of the assembly line and the number of defects per unit was recorded. For the first 100 cars produced, there were 40 defective

asked by Anonymous on July 7, 2017
5. ### Math

Please help me.... Two cars are starting from positions that are 20 miles apart. They are both headed for the same intersection, as depicted in the diagram below. Car A is traveling at 30 mph, and Car B is traveling at 45 mph.

asked by Lizzie098 on January 8, 2014
6. ### Probability

Problem 1. Starting at time 0, a red bulb flashes according to a Poisson process with rate λ=1 . Similarly, starting at time 0, a blue bulb flashes according to a Poisson process with rate λ=2 , but only until a nonnegative

asked by AK on May 16, 2020