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  2. Chebyshev's inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_inequality

    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."

  3. Coupon collector's problem - Wikipedia

    en.wikipedia.org/wiki/Coupon_collector's_problem

    In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...

  4. 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]

  5. 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.

  6. Chebyshev's sum inequality - Wikipedia

    en.wikipedia.org/wiki/Chebyshev's_sum_inequality

    In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if ...

  7. Chernoff bound - Wikipedia

    en.wikipedia.org/wiki/Chernoff_bound

    It is a sharper bound than the first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, when applied to sums the Chernoff bound requires the random variables to be independent, a condition that is not required by either Markov's inequality or ...

  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. 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.