Dear all,(adsbygoogle = window.adsbygoogle || []).push({});

I wonder wheather there exsits a probability inequality for the sum of independent normal random variables ([itex]X_i[/itex] are i.i.d. normal random varianble with mean [itex]\mu[/itex] and variance [itex]\sigma^2[/itex]):

[itex]

P\left(\frac{1}{n}\sum_{i=1}^n X_i - \mu> \epsilon\right)\leq

f(\epsilon, \sigma^2,n) \right).

[/itex]

We know that Bernstein inequality is for the sum of bounded random variables:

[itex]

P\left(\frac{1}{n}\sum_{i=1}^n X_i -\mu > \epsilon\right)\leq

\exp\left(-\frac{n\epsilon^2}{2\sigma^2+ 2c\epsilon/3} \right).

[/itex]

I wonder whether there is some similar inequality for normal variables.

Thanks!

Phonic

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

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

# Probability inequality for the sum of independent normal random variables

Loading...

Similar Threads - Probability inequality independent | Date |
---|---|

I Probability of getting 3 out of 4 numbers correct | Today at 2:40 AM |

B Probability and Death Sentences | Thursday at 10:48 PM |

B Probability of loto hitting a specific place | Mar 10, 2018 |

A basic probability inequality | Oct 22, 2009 |

Probability theoretic inequality | Jul 21, 2008 |

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