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 | Science Articles, Homework Help, Discussion**

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!

# Probability inequality for the sum of independent normal random variables

**Physics Forums | Science Articles, Homework Help, Discussion**