# Bhatia–Davis inequality

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In mathematics, the **Bhatia–Davis inequality**, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance *σ*^{2} of any bounded probability distribution on the real line.

Suppose a distribution has minimum *m*, maximum *M*, and expected value *μ*. Then the inequality says:

Equality holds precisely if all of the probability is concentrated at the endpoints *m* and *M*.

The Bhatia–Davis inequality is stronger than Popoviciu's inequality on variances.

## See alsoEdit

## ReferencesEdit

- Bhatia, Rajendra; Davis, Chandler (April 2000). "A Better Bound on the Variance".
*American Mathematical Monthly*. Mathematical Association of America.**107**(4): 353–357. doi:10.2307/2589180. ISSN 0002-9890. JSTOR 2589180.

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