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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.
- 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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