Inequality of Chernoff

In Probability, the inequality of Chernoff , according to Hermann Chernoff, states the following result: that is to say

$X\_1,\; X\_2,\; \backslash \; dowries,\; X\_n$

a whole of random variable independent, such as

$E=0$

and

$\backslash \; left|X\_i\; \backslash \; right|\backslash \; Leq\; 1\; \backslash ,$ for all I .

That is to say

$X=\backslash sum\_\{i=1\}^n\; X\_i$

and σ ² the Variance of X . Then, one a:

$P\; (\backslash \; left|X\; \backslash \; right|\backslash \; geq\; K\; \backslash \; sigma)\; \backslash \; Leq\; 2e^\; \{-\; k^2/4n\}$

for all

$0\; \backslash \; Leq\; K\; \backslash \; Leq\; 2\; \backslash \; sigma.\; \backslash ,$

See too

• Terminals of Chernoff: Case generalizing this inequality

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