What is a Poisson Distribution

A Poisson distribution is a type of probability distribution that describes the probability of a given number of events occurring in a fixed period of time or space, given the average number of events per unit of time or space. It is often used to model the number of times an event occurs in a given time period, such as the number of customers arriving at a store in an hour, the number of telephone calls received by a call center in a day, or the number of particles detected in a sample.
The Poisson distribution is defined by a single parameter, lambda (λ), which represents the average number of events per unit of time or space. The probability of a given number of events occurring in a given period of time or space is given by the following formula:
P(k) = (λ^k * e^-λ) / k!


where:

• P(k) is the probability of k events occurring in the given period of time or space
• λ is the average number of events per unit of time or space
• k is the number of events
• e is the base of the natural logarithm (approximately 2.71828)
• k! is the factorial of k (the product of all positive integers from 1 to k)

The Poisson distribution is a useful tool for modeling the probability of events occurring in a given time period when the average number of events per unit of time is known. It is often used in fields such as engineering, finance, and biology to model the occurrence of events such as defects, accidents, or mutations.