## 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.