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  2. Chebyshev's inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_inequality

    For n = 2 we obtain Chebyshev's inequality. For k ≥ 1, n > 4 and assuming that the n th moment exists, this bound is tighter than Chebyshev's inequality. [citation needed] This strategy, called the method of moments, is often used to prove tail bounds.

  3. Chebyshev–Markov–Stieltjes inequalities - Wikipedia

    en.wikipedia.org/wiki/Chebyshev–Markov...

    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]

  4. Chebyshev's sum inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_sum_inequality

    In mathematics, Chebyshev's sum inequality, ... The two sequences are non-increasing, therefore a j − a k and b j − b k have the same sign for any j, ...

  5. List of inequalities - Wikipedia

    en.wikipedia.org/wiki/List_of_inequalities

    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; Friedrichs's inequality; Gagliardo–Nirenberg interpolation inequality; Gårding's inequality; Grothendieck inequality ...

  6. 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.

  7. Law of large numbers - Wikipedia

    en.wikipedia.org/wiki/Law_of_large_numbers

    5.1 Proof using Chebyshev's inequality assuming finite variance. 5.2 Proof using convergence of characteristic functions. 6 Proof of the strong law. 7 Consequences.

  8. Chebyshev's theorem - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_theorem

    Chebyshev's sum inequality, about sums and products of decreasing sequences Chebyshev's equioscillation theorem , on the approximation of continuous functions with polynomials The statement that if the function π ( x ) ln ⁡ x / x {\textstyle \pi (x)\ln x/x} has a limit at infinity, then the limit is 1 (where π is the prime-counting function).

  9. Markov's inequality - Wikipedia

    en.wikipedia.org/wiki/Markov's_inequality

    Markov's inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a random variable. Markov's inequality can also be used to upper bound the expectation of a non-negative random variable in terms of its distribution function.