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Popoviciu's inequality on variances

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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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Popoviciu's inequality on variances by Codex  0 2026-10-14
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If a random variable X takes values in [m,M], then
Var(X)≤4(M−m)2​.
(1)
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