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

X₁,X₂,...,X_n

be independent random variables, such that

E[X_i] = 0

and

for all i.

Let

and let σ² be the variance of X_i. Then

for any

where σ is the standard deviation of the random variable X_i.

See also

• Chernoff bound: a special case of this inequality