In probability theory, Etemadi's inequality is a so-called "maximal inequality", an inequality that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound. The result is due to Nasrollah Etemadi.
Let X<sub>1</sub>, ..., X<sub>n</sub> be independent real-valued random variables defined on some common probability space, and let ñ âÂÂ¥ 0. Let S<sub>k</sub> denote the partial sum
Then
Suppose that the random variables X<sub>k</sub> have common expected value zero. Apply Chebyshev's inequality to the right-hand side of Etemadi's inequality and replace ñ by ñ / 3. The result is Kolmogorov's inequality with an extra factor of 27 on the right-hand side: