Enter the average rate of value per interval and the actual number of events into the calculator to determine the probability in a Poisson process.

## Poisson Process Formula

The following formula is used to calculate the probability in a Poisson process.

P(X=k) = (λ^k * e^{-λ}) / k!

Variables:

• P(X=k) is the probability of k events in an interval λ is the average rate of value per interval k is the actual number of events that result e is the base of the natural logarithm (approximately equal to 2.71828) k! is the factorial of k

To calculate the probability in a Poisson process, raise the average rate of value per interval (λ) to the power of the actual number of events that result (k), then multiply the result by the base of the natural logarithm (e) raised to the power of the negative average rate of value per interval (-λ). Divide this result by the factorial of the actual number of events that result (k!).

## What is a Poisson Process?

A Poisson Process is a mathematical model used to describe events that occur independently and at a constant average rate within a given unit of time or space. It is named after the French mathematician Siméon Denis Poisson. This process is often used in fields such as telecommunications, finance, and environmental science to predict the probability of a certain number of events happening in a fixed interval of time or space.