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:
“Nature seems at each man’s birth to have marked out the bounds of his virtues and vices, and to have determined how good or how wicked that man shall be capable of being.”
—François, Duc De La Rochefoucauld (1613–1680)