- #1
phonic
- 28
- 0
Dear all,
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
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