Chebyshev's inequality

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Related to Chebyshev inequality: variance, Markov inequality

Chebyshev's inequality

(ˈtʃɛbɪˌʃɒfs)

(Statistics) statistics the fundamental theorem that the probability that a random variable differs from its mean by more than k standard deviations is less than or equal to 1/k²

[named after P. L. Chebyshev (1821–94), Russian mathematician]

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Tchebychev's inequality

References in periodicals archive ?

By virtue of Chebyshev inequality, we can easily obtain that the solution (x(t), y(t), z(t)) of system (4) is stochastically ultimately bounded.

Dynamics of a stochastic cooperative predator-prey system with Beddington-DeAngelis functional response

Confidence bounds can also be established through use of the Chebyshev inequality [5], although these bounds tend to be too large for practical use [6].

Online stochastic convergence analysis of the Kalman filter

Hence, by Chebyshev inequality, we have for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].