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| | In [[probability theory]], '''Popoviciu's inequality''', named after [[Tiberiu Popoviciu]]{{Citation needed|date=August 2009}}, is an [[upper bound]] on the [[variance]] of any bounded [[probability distribution]]. Let ''M'' and ''m'' be upper and lower bounds on the values of any [[random variable]] with a particular probability distribution. Then Popoviciu's inequality states:{{Citation needed|date=August 2009}} |
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| | : <math> \text{variance} \le \frac14 (M - m)^2. </math> |
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| | Equality holds precisely when half of the probability is concentrated at each of the two bounds. |
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| | Popoviciu's inequality is weaker than the [[Bhatia–Davis inequality]]. |
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| | {{DEFAULTSORT:Popoviciu's Inequality On Variances}} |
| | [[Category:Theory of probability distributions]] |
| | [[Category:Statistical inequalities]] |
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| | {{probability-stub}} |
Revision as of 18:05, 20 March 2013
In probability theory, Popoviciu's inequality, named after Tiberiu PopoviciuPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park., is an upper bound on the variance of any bounded probability distribution. Let M and m be upper and lower bounds on the values of any random variable with a particular probability distribution. Then Popoviciu's inequality states:Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
Equality holds precisely when half of the probability is concentrated at each of the two bounds.
Popoviciu's inequality is weaker than the Bhatia–Davis inequality.
Template:Probability-stub