Bias
Abstract
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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.
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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.
Key concepts: Mathematics, Multidimensional Chebyshev's inequality, Chebyshev's inequality, Chebyshev filter, Markov's inequality, Mathematical analysis, Boundary (topology), Class (philosophy)