# ⓘ Bhatia–Davis inequality. In mathematics, the Bhatia–Davis inequality, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance σ 2 of a ..

## ⓘ Bhatia–Davis inequality

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:

σ 2 ≤ M − μ − m. {\displaystyle \sigma ^{2}\leq M-\mu\mu -m.\,}

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

The Bhatia–Davis inequality is stronger than Popovicius inequality on variances.

• geometry and matrix analysis. He is one of the eponyms of the Bhatia Davis inequality Rajendra Bhatia founded the series Texts and Readings in Mathematics in
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•  2071. Attwood 2005. Srivastava 1968. Sen 1982. Bhatia 1985. Mander 2009, p. 1. Davis 2001, p. 299. Davis 2001, pp. 299 300. Wong 1998. Martin Ravallion
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