## Binomial Distribution Calculator

Binomial distribution calculator is used to find the probability and cumulative probabilities for binomial random variable given the number of trials ($n$) and probability of success ($p$).

Binomial Distribution Calculator | |
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Number of trials ($n$): | |

Number of success (x): | |

Probability of success ($p$): | |

Result | |

Mean : $np$ | |

Variance : $np(1-p)$ | |

Probability : P(X = x) | |

Cumulative Probability : P(X ≤ x) | |

Cumulative Probability : P(X < x) | |

Cumulative Probability : P(X ≥ x) | |

Cumulative Probability : P(X > x) | |

## Binomial Distribution

The probability mass function of Binomial distribution with parameter $n$ and $p$ is

```
$$
\begin{aligned}
P(X=x)&=\binom{n}{x} p^x q^{n-x},\\
& \quad x=0,1,2,\cdots, n;\\
& \quad 0<p<1,q=1-p
\end{aligned}
$$
```

where

- $n =$ number of trials,
- $x =$ number of successes in $n$ trials,
- $p =$ probability of success,
- $q = 1- p =$ probability of failures.