@article {10.3844/jmssp.2010.47.51, article_type = {journal}, title = {Boundary Distributions with Respect to Chebyshev's Inequality}, author = {Bias, Peter and Hedman, Shawn and Rose, David}, volume = {6}, year = {2010}, month = {Mar}, pages = {47-51}, doi = {10.3844/jmssp.2010.47.51}, url = {https://thescipub.com/abstract/jmssp.2010.47.51}, abstract = {Variables 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 = {Journal of Mathematics and Statistics}, publisher = {Science Publications} }