Research ArticleOpen accessIn the keywordsBoundary Distributions with Respect to Chebyshev's InequalityPeter Bias, Shawn Hedman, David RoseVariables whose distributions achieve the boundary value of Chebyshev’s inequality are characterized and it is found that non-constant variables with this property are symmetric discrete with at most three values. Nevertheless, the bound of Chebyshev’s inequality remains optimal for the class of continuous variables. …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 8,633 accessesView PDFCite