Question

The number of traffic accidents at a certain intersection is thought to be well modeled by...

The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3.5 accidents per year

If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?

Homework Answers

Answer #1

Answer:-

let the number of accidents that occur in a year be X.Then we are given that

X~Poisson(3.5)

Poisson distribution follows a memoryless property therefore the probability that there will be an accident next year given there was no accident in last 6 months is equal to the probability of an accident in the next year without any condition.

Let be the number of accident in next year .Then we get:

Y~Poisson(3.5)

Therefore we simply have to find:

Therefore poisson distribution probability formula we get:

Therefore 0.9699 is the required probability

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The number of traffic accidents in a certain area follows a Poisson process with a rate...
The number of traffic accidents in a certain area follows a Poisson process with a rate of 1.5 per hour between 8:00 A.M. and 5:00 P.M. during the normal working hours in a working day. Compute the following probabilities. There will be no traffic accident between 11:30 AM to 12:00 PM. There will be more than 3 traffic accidents after 3:45 P.M. There will be in between 15 and 18 traffic accident during the normal working hours in a working...
The number of accidents that occur at a busy intersection is Poisson distributed with a mean...
The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.9 per week. Find the probability of the following events. A. No accidents occur in one week. Probability = B. 3 or more accidents occur in a week. Probability = C. One accident occurs today. Probability =
The number of accidents in a certain city is modeled by a Poisson random variable with...
The number of accidents in a certain city is modeled by a Poisson random variable with average rate of 10 accidents per day. Suppose that the number of accidents in different days are independent. Use the central limit theorem to find the probability that there will be more than 3800 accidents in a certain year. Assume that there are 365 days in a year
15) The number of traffic accidents that occur on a particular stretch of road during a...
15) The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.5. Find the probability that exactly four accidents will occur on this stretch of road each of the next two months. A) 0.044255                            B) 0.088510                            C) 0.001958                            D) 0.000144 27) A machine is set to pump cleanser into a process at the rate of 10 gallons per minute. Upon inspection, it is...
Suppose that the number of accidents occurring on a highway per hour follows a Poisson distribution...
Suppose that the number of accidents occurring on a highway per hour follows a Poisson distribution with a mean of 1.25. What is the probability of exactly three accidents occur in hour? What is the probability of less than two accidents in ten minutes? What is the probability that the time between two successive accidents is at least ten minutes? If ten minutes have gone by without an accident, what is the probability that an accident will occur in the...
Suppose that the number of accidents occurring on a highway per hour follows a Poisson distribution...
Suppose that the number of accidents occurring on a highway per hour follows a Poisson distribution with a mean of 1.25. What is the probability of exactly three accidents occur in hour? What is the probability of less than two accidents in ten minutes? What is the probability that the time between two successive accidents is at least ten minutes? If ten minutes have gone by without an accident, what is the probability that an accident will occur in the...
Car accidents at a certain intersection are randomly distributed in time according to a Poisson process,...
Car accidents at a certain intersection are randomly distributed in time according to a Poisson process, with 7 accidents per week on average. If there were 3 accidents in a 2-week period, what is the probability there were 2 accidents in the first 1 of these 2 weeks? (4 decimal accuracy please)
Car accidents at a certain intersection are randomly distributed in time according to a Poisson process,...
Car accidents at a certain intersection are randomly distributed in time according to a Poisson process, with 5 accidents per week on average. What is the probability that there are 1 accidents in the first 1 week period and 1 more in the second 1 week period.? (4 decimal accuracy please)
There is an average of four accidents per year at a particular intersection. What is the...
There is an average of four accidents per year at a particular intersection. What is the probability of more than one accident there next month? Hint: Use 1 month = 1/12 of a year to first get the number of accidents that are expected next month.
The average number of traffic accidents on a certain section of highway is two per week....
The average number of traffic accidents on a certain section of highway is two per week. a. Find the probability that three or more accidents happen during a one-week period. b. Find the standard deviation for the number of traffic accidents.