## Bernoulli Distribution Calculator

Bernoulli’s distribution calculator can help you to determine the mean, variance and probability for Bernoulli’s distribution with parameter probability of success $p$.

Bernoulli Distribution Calculator | |
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Probability of success (p): | |

Number of success (x): | |

Result | |

Probability : P(X = x) | |

Mean : E(X) | |

Variance : V(X) | |

Standard Deviation : | |

## Definition of Bernoulli Distribution

A discrete random variable $X$ is said to have Bernoulli distribution with parameter $p$ if its probability mass function is

$$
\begin{aligned}
P(X=x)&=p^x (1-p)^{1-x},\hbox{$x=0,1$;}

& \hbox{$0<p<1$}.

\end{aligned}
$$

where

- $x =$ number of successes in single trial,
- $p =$ probability of success,