Popoviciu's inequality on variances

If a random variable

X

takes values in

[m, M]

, then

Var (X) \leq \frac{( M - m ) ^{2}}{4} .

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Hoeffding lemma

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Popoviciu's inequality is a result in statistics concerning the variances of random variables. Specifically, it provides a bound on the variance of a random variable in relation to its range.

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