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In probability theory, Popoviciu's inequality, named after Tiberiu Popoviciu, 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: : Sharma et al. have proved an improvement of the Popoviciu's inequality that says that: : 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. ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Popoviciu's inequality on variances」の詳細全文を読む スポンサード リンク
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