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:
“What comes over a man, is it soul or mind
That to no limits and bounds he can stay confined?
You would say his ambition was to extend the reach
Clear to the Arctic of every living kind.
Why is his nature forever so hard to teach
That though there is no fixed line between wrong and right,
There are roughly zones whose laws must be obeyed?”
—Robert Frost (1874–1963)