 ##  [Chernoff Bound](/chernoff-bound) 

  ##  [Chernoff Bound](https://natural.quantumdictionary.io/chernoff-bound-0) 

  
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**Natural &amp; Formal Sciences Dictionary**

 
Definition

An exponential upper bound on the tail probability of a sum of random variables obtained by optimizing Markov's inequality applied to a moment-generating function; it quantifies how unlikely large deviations are.

 
 ##  [Chernoff Bound](https://mathlogic.quantumdictionary.io/chernoff-bound-1) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

An exponential upper bound on tail probabilities for random sums or aggregates obtained by applying Markov's inequality to a moment-generating function (MGF) and optimizing the exponential tilt: for S a sum, P(S ≥ t) ≤ inf_{s&gt;0} e^{-s t} E[e^{s S}].