# Cauchy random variable

$X$ is a Cauchy random variable with parameters $\theta \in \mathbb{R}$ and $\beta >0\in \mathbb{R}$, commonly denoted $X\sim Cauchy(\theta ,\beta )$ if

${f}_{X}(x)={\displaystyle \frac{1}{\pi \beta [1+{(\frac{x-\theta}{\beta})}^{2}]}}.$ |

Cauchy random variables are used primarily for theoretical purposes, the key point being that the values $E[X]$ and $Var[X]$ are undefined for Cauchy random variables.

Title | Cauchy random variable |
---|---|

Canonical name | CauchyRandomVariable |

Date of creation | 2013-03-22 11:54:32 |

Last modified on | 2013-03-22 11:54:32 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 11 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 60A10 |

Synonym | Cauchy distribution |