# Chebyshev’s inequality

Let $X\in {\text{\mathbf{L}}}^{2}$ be a real-valued random variable^{} with mean $\mu =\mathbb{E}[X]$ and variance ${\sigma}^{2}=\mathrm{Var}[X]$. Then for any standard of accuracy $t>0$,

$$\mathbb{P}\left\{\right|X-\mu |\ge t\}\le \frac{{\sigma}^{2}}{{t}^{2}}.$$ |

Note: There is another Chebyshev’s inequality (http://planetmath.org/ChebyshevsInequality), which is unrelated.

Title | Chebyshev’s inequality |
---|---|

Canonical name | ChebyshevsInequality |

Date of creation | 2013-03-22 12:47:55 |

Last modified on | 2013-03-22 12:47:55 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 6 |

Author | rspuzio (6075) |

Entry type | Theorem |

Classification | msc 60A99 |

Related topic | MarkovsInequality |

Related topic | ChebyshevsInequality |