Chernoff Bounds
If the random variables may also be assumed to be independent, it is possible to obtain sharper bounds. Let δ > 0. Then
With this inequality it can be shown that
where μ is the mean of the distribution. Further discussion may be found in the article on Chernoff bounds
Read more about this topic: Chebyshev's Inequality
Famous quotes containing the word bounds:
“How far men go for the material of their houses! The inhabitants of the most civilized cities, in all ages, send into far, primitive forests, beyond the bounds of their civilization, where the moose and bear and savage dwell, for their pine boards for ordinary use. And, on the other hand, the savage soon receives from cities iron arrow-points, hatchets, and guns, to point his savageness with.”
—Henry David Thoreau (1817–1862)