Poisson probability distribution

Definition

The Poisson probability distribution models the number of times an event occurs within a fixed interval of time or space. It is characterized by the average rate at which events occur, denoted by $\lambda$ (lambda).

5 Must Know Facts For Your Next Test

1. The Poisson distribution assumes that events occur independently.
2. The mean and variance of a Poisson distribution are both equal to $\lambda$.
3. The probability mass function (PMF) of a Poisson distribution is given by $P(X=k)=\frac{e^{-\lambda} \lambda^k}{k!}$, where $k$ is the number of occurrences.
4. Poisson distributions are often used for modeling rare events over continuous intervals.
5. As $\lambda$ increases, the shape of the Poisson distribution approaches that of a normal distribution.

Related terms

Discrete Random Variable:

A variable that can take on a countable number of distinct values.

Exponential Distribution:

A continuous probability distribution often used to model the time between independent events that happen at a constant average rate.

$\lambda$ (Lambda): The average rate at which events occur in a Poisson process; also serves as both the mean and variance in a Poisson distribution.