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.
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.
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.
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.
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.
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.
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.