Boundary Distributions with Respect to Chebyshev's Inequality

2010 Journal of Mathematics and Statistics  
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.
doi:10.3844/jmssp.2010.47.51 fatcat:p7g6ndq57zf4zeak4s6lv6ufau