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The term Chebyshev's inequality may also refer to Markov's inequality, especially in the context of analysis. They are closely related, and some authors refer to Markov's inequality as "Chebyshev's First Inequality," and the similar one referred to on this page as "Chebyshev's Second Inequality."
In probability theory, the multidimensional Chebyshev's inequality [1] is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount.
Toggle the table of contents. Chebyshev's sum inequality. 15 languages. ... In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, ...
In fact, Chebyshev's proof works so long as the variance of the average of the first n values goes to zero as n goes to infinity. [15] As an example, assume that each random variable in the series follows a Gaussian distribution (normal distribution) with mean zero, but with variance equal to 2 n / log ( n + 1 ) {\displaystyle 2n/\log(n+1 ...
Toggle the table of contents. ... Chebyshev's bias is the phenomenon that most of ... For example, this inequality holds for all primes x < 26833 except 5, 17 ...
Cantelli's inequality; Chebyshev's inequality; Chernoff's inequality; Chung–Erdős inequality; Concentration inequality; Cramér–Rao inequality; Doob's martingale inequality; Dvoretzky–Kiefer–Wolfowitz inequality; Eaton's inequality, a bound on the largest absolute value of a linear combination of bounded random variables; Emery's ...
In mathematical analysis, the Chebyshev–Markov–Stieltjes inequalities are inequalities related to the problem of moments that were formulated in the 1880s by Pafnuty Chebyshev and proved independently by Andrey Markov and (somewhat later) by Thomas Jan Stieltjes. [1]
Bernstein inequalities (probability theory) Binomial regression; Binomial proportion confidence interval; Chebyshev's inequality; Chernoff bound; Gauss's inequality; Markov's inequality; Rule of succession; Rule of three (medicine) Vysochanskiï–Petunin inequality