## Poisson Distribution Calculator

Poisson distribution calculator is used to find the probability and cumulative probabilities for Poisson random variable given the mean number of successes ($\lambda$).

Poisson Distribution Calculator
Average rate of success ($\lambda$):
Number of success (x):
Result
Probability : P(X = x)
Cumulative Probability : P(X ≤ x)
Cumulative Probability : P(X < x)
Cumulative Probability : P(X ≥ x)
Cumulative Probability : P(X > x)

## Poisson Distribution

A discrete random variable $X$ is said to have Poisson distribution with parameter $\lambda$ if its probability mass function is

\begin{aligned} P(X=x)& =\frac{e^{-\lambda}\lambda^x}{x!},\ & \hbox{x=0,1,2,\cdots;\lambda>0.} \ \end{aligned}

where

• $\lambda=$ mean number of successes.