Calculating Poisson Distribution for Telephone Calls in College Switchboard

In summary, the probability of waiting more than 1.5 minutes for the second call is 9/8*(1-0.75)/0.75 = (1-0.06)/0.06 = 99.8%.
  • #1
XodoX
203
0

Homework Statement


Telephone calls enter a college switchboard according to a Poisson process on the average of three calls every 4 minutes (i.e., at a rate of λ=0.75 per minute). Let W denote the waiting time in minutes until the second call. Compute P(W>1.5 minutes).


Homework Equations





The Attempt at a Solution



I don't get it. No idea how to do it. I guess 1.5 means here that at the most 1 event can occur here.
 
Physics news on Phys.org
  • #2
XodoX said:

Homework Statement


Telephone calls enter a college switchboard according to a Poisson process on the average of three calls every 4 minutes (i.e., at a rate of λ=0.75 per minute). Let W denote the waiting time in minutes until the second call. Compute P(W>1.5 minutes).


Homework Equations





The Attempt at a Solution



I don't get it. No idea how to do it. I guess 1.5 means here that at the most 1 event can occur here.

You DO know how to do it. Your guess is correct: do you see why?

RGV
 
  • #3
No, I don't. The poisson distribution is not in this chapter. It's Weibull, Gompertz, extreme value, gamma, chi-square, and logonormal. I don't know which one of those it is.
 
  • #4
XodoX said:
No, I don't. The poisson distribution is not in this chapter. It's Weibull, Gompertz, extreme value, gamma, chi-square, and logonormal. I don't know which one of those it is.

Well, it's related to the Gamma.

However, let me ask you: what does the Poisson distribution represent? Never mind if it is not in that chapter; it is either in another chapter or else in another book or else in thousands of web pages. So, you have a Poisson distribution with m = 1.5*0.75 = 9/8 = 1.125; that would be the expected number of calls to occur in a 1.5 minute period. You can find the probability distribution of the number of calls in a 1.5-minute period by using the Poisson distribution formula for mean m. Now ask: if you need to wait > 1.5 min for the second call, how many have arrived before time 1.5? What is the probability of that?

RGV
 
Last edited:

FAQ: Calculating Poisson Distribution for Telephone Calls in College Switchboard

What is a Poisson distribution?

A Poisson distribution is a probability distribution that describes the number of times an event occurs in a fixed interval of time or space, when the event occurs independently and at a constant rate. It is often used to model rare events, such as the number of accidents in a day or the number of customers arriving at a store in an hour.

What are the characteristics of a Poisson distribution?

A Poisson distribution is characterized by two parameters: lambda (λ), which represents the average rate of events occurring in a given time or space, and the interval of time or space in which the events occur. It is also a discrete distribution, meaning that the possible outcomes are countable and have gaps between them.

How is a Poisson distribution different from a normal distribution?

A normal distribution is a continuous distribution that is symmetrical and bell-shaped, while a Poisson distribution is a discrete distribution that is right-skewed. Additionally, a normal distribution can take on any value from negative infinity to positive infinity, while a Poisson distribution can only take on non-negative integer values.

What are some real-world applications of Poisson distribution?

Poisson distribution is commonly used in fields such as physics, biology, economics, and engineering to model events that occur at a constant rate, such as radioactive decay, insect population growth, customer arrivals, and machine failures. It is also used in insurance and risk analysis to calculate the probability of rare events, such as natural disasters or accidents.

Can a Poisson distribution be used to model events that do not occur at a constant rate?

No, a Poisson distribution is only appropriate for events that occur at a constant rate. If the rate of events changes over time or space, a different distribution, such as a binomial or exponential distribution, may be more suitable.

Similar threads

Solving Poisson Distribution Problems: Questions on Calls/Minute
Replies
2
Views
1K
Exercise on Poisson distribution
Replies
3
Views
2K
Probability and pedestrian wait time density function
Replies
32
Views
2K
Binomial -> Poisson distribution question
Replies
10
Views
2K
How Does the PDF of Wait Time Vary for Pedestrians at a Traffic Signal?
2
Replies
56
Views
4K
What Is the Expected Wait Time for the Last Pedestrian at a Traffic Light?
Replies
2
Views
1K
Statistics question (poisson distribution, multivariate )
Replies
1
Views
2K
Understanding the Characteristic Function in Solving Poisson Process Problems
Replies
2
Views
2K
I Difference between Time, Arrival-Time & Inter-Arrival-Time in Poisson Process
Replies
8
Views
2K
Bayesian inference of Poisson likelihood and exponential prior.
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top