# Chernoff's inequality

This article needs attention from an expert in Mathematics. |

In probability theory, **Chernoff's inequality**, named after Herman Chernoff, states the following. Let

be independent random variables, such that

and

- for all
*i*.

Let

and let σ^{2} be the variance of *X*. Then

for any

## See also

- Chernoff bounds: the general case
- Chernoff bound: a special case of this inequality