Question

Consider a Poisson process with rate λ and let L be the time of the last...

Consider a Poisson process with rate λ and let L be the time of the last arrival in the interval [0, t], with L = 0 if there was no arrival. (a) Compute E(t − L). (b) What happens when we let t → ∞ in the answer to (a)?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose passengers arrive at a MARTA station between 10am-5pm following a Poisson process with rate λ=...
Suppose passengers arrive at a MARTA station between 10am-5pm following a Poisson process with rate λ= 60 per hour. For notation, let N(t) be the number of passengers arrived in the first t hours, S0= 0 , Sn be the arrival time of the nth passenger, Xn be the interrarrival time between the (n−1)st and nth passenger. a. What is the probability that ten passengers arrive between 2pm and 4pm given that no customer arrive in the first half hour?...
People arrive according to a Poisson process with rate λ, with each person independently being equally...
People arrive according to a Poisson process with rate λ, with each person independently being equally likely to be either a man or a woman. If a woman (man) arrives when there is at least one man (woman) waiting, then the woman (man) departs with one of the waiting men (women). If there is no member of the opposite sex waiting upon a person’s arrival, then that person waits. Let X(t) denote the number waiting at time t. Argue that...
Exercise: The sum of Poisson r.v.'s 1 point possible (graded) Consider a Poisson process with rate...
Exercise: The sum of Poisson r.v.'s 1 point possible (graded) Consider a Poisson process with rate λ=1. Consider three times that satisfy 0<t1<t2<t3. Let M be the number of arrivals during the interval [0,t2]. Let N be the number of arrivals during the interval [t1,t3]. Is the random variable M+N guaranteed to be Poisson?
Q1.    Select an arrival (Poisson) process on any time interval (eg.: second, minute, hour, day, week,...
Q1.    Select an arrival (Poisson) process on any time interval (eg.: second, minute, hour, day, week, month, etc….) as you like. Possible arrival processes could be arrival of signal, click, broadcast, defective product, customer, passenger, patient, rain, storm, earthquake etc.[Hint: Poisson and exponential distributions exits at the same time.] Collect approximately n=30 observations per unit time interval. .[Hint: Plot your observations. If there is sharp increase or decrease then you could assume that you are observing arrivals according to proper...
Select an arrival (Poisson) process on any time interval (eg.: second, minute, hour, day, week, month,...
Select an arrival (Poisson) process on any time interval (eg.: second, minute, hour, day, week, month, etc….) as you like. Possible arrival processes could be arrival of signal, click, broadcast, defective product, customer, passenger, patient, rain, storm, earthquake etc.[Hint: Poisson and exponential distributions exits at the same time.] Collect approximately n=30 observations per unit time interval. .[Hint: Plot your observations. If there is sharp increase or decrease then you could assume that you are observing arrivals according to proper Poisson...
Vehicles arrive at a small bridge according to a Poisson process with arrival rate l =...
Vehicles arrive at a small bridge according to a Poisson process with arrival rate l = 900 veh/hr. a. What are the mean and the variance of the number of arrivals during a 30 minutes interval? b. What is the probability of 0 cars arriving during a 4 second interval? c. A pedestrian arrives at a crossing point just after a car passed by. If the pedestrian needs 4 sec to cross the street, what is the probability that a...
Starting at time 0, a red bulb flashes according to a Poisson process with rate ?=1....
Starting at time 0, a red bulb flashes according to a Poisson process with rate ?=1. Similarly, starting at time 0, a blue bulb flashes according to a Poisson process with rate ?=2, but only until a nonnegative random time ?, at which point the blue bulb “dies." We assume that the two Poisson processes and the random variable ? are (mutually) independent. Suppose that X is equal to either 1 or 2, with equal probability. Write down an expression...
Jane observes a Poisson Process for 15 hours and counts a total of 840 successes. Let...
Jane observes a Poisson Process for 15 hours and counts a total of 840 successes. Let λ denote the rate per hour for the Poisson Process. Use Jane’s data to obtain the approximate 95% confidence interval estimate of λ.
Starting at time 0, a red bulb flashes according to a Poisson process with rate ?=1...
Starting at time 0, a red bulb flashes according to a Poisson process with rate ?=1 . Similarly, starting at time 0, a blue bulb flashes according to a Poisson process with rate ?=2 , but only until a nonnegative random time ? , at which point the blue bulb “dies." We assume that the two Poisson processes and the random variable ? are (mutually) independent. Suppose that ? is equal to either 1 or 2, with equal probability. Write...
At a train station, international trains arrive at a rate λ = 1 (poisson distribution). At...
At a train station, international trains arrive at a rate λ = 1 (poisson distribution). At the same train station national trains arrive at rate λ = 2 (poisson distribution). The two trains are independent. What is the probability that the first international train arrives within 3 times the arrival time of the first national train?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT