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  2. Chebyshev's inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_inequality

    In probability theory, Chebyshev's inequality ... A table of values for the Saw–Yang–Mo inequality for finite sample sizes (N < 100) has been determined by Konijn.

  3. Multidimensional Chebyshev's inequality - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_Chebyshev...

    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.

  4. Chebyshev's sum inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_sum_inequality

    Toggle the table of contents. Chebyshev's sum inequality. 15 languages. ... In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, ...

  5. Law of large numbers - Wikipedia

    en.wikipedia.org/wiki/Law_of_large_numbers

    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 ...

  6. Outline of probability - Wikipedia

    en.wikipedia.org/wiki/Outline_of_probability

    Jensen's inequality; General moments about the mean; Correlated and uncorrelated random variables; Conditional expectation: law of total expectation, law of total variance; Fatou's lemma and the monotone and dominated convergence theorems; Markov's inequality and Chebyshev's inequality

  7. List of inequalities - Wikipedia

    en.wikipedia.org/wiki/List_of_inequalities

    Bessel's inequality; Bihari–LaSalle inequality; Bohnenblust–Hille inequality; Borell–Brascamp–Lieb inequality; Brezis–Gallouet inequality; Carleman's inequality; Chebyshev–Markov–Stieltjes inequalities; Chebyshev's sum inequality; Clarkson's inequalities; Eilenberg's inequality; Fekete–Szegő inequality; Fenchel's inequality ...

  8. Chebyshev's theorem - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_theorem

    Chebyshev's theorem is any of several theorems proven by Russian mathematician Pafnuty Chebyshev. Bertrand's postulate, that for every n there is a prime between n and 2n. Chebyshev's inequality, on the range of standard deviations around the mean, in statistics; Chebyshev's sum inequality, about sums and products of decreasing sequences

  9. Vysochanskij–Petunin inequality - Wikipedia

    en.wikipedia.org/wiki/Vysochanskij–Petunin...

    The theorem refines Chebyshev's inequality by including the factor of 4/9, made possible by the condition that the distribution be unimodal. It is common, in the construction of control charts and other statistical heuristics, to set λ = 3 , corresponding to an upper probability bound of 4/81= 0.04938..., and to construct 3-sigma limits to ...