The "first central moment" of a real-valued function(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\mu_1 \equiv \int_{-\infty}^\infty (x - \mu) f(x)\,dx = 0[/tex]

where

[tex]\mu \equiv \int_{-\infty}^\infty x\, f(x)\,dx[/tex]

so we have

[tex]\int_{-\infty}^\infty (x - \left ( \int_{-\infty}^\infty x\, f(x)\,dx \right ) ) f(x)\,dx = 0[/tex]

Intuitively, it seems to make sense, but how do we manipulate those integrals to prove this equality?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# First central moment

Loading...

Similar Threads - central moment | Date |
---|---|

A Angular Moment Operator Vector Identity Question | Feb 10, 2018 |

A Moments of normal distribution | Jan 6, 2017 |

Central angle of a cone? | Aug 12, 2010 |

Fourier transform in central and difference coordinates | Dec 8, 2009 |

What does the central thm of calculus of variation says? | Aug 3, 2006 |

**Physics Forums - The Fusion of Science and Community**