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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. 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'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 ...

  5. Analytic number theory - Wikipedia

    en.wikipedia.org/wiki/Analytic_number_theory

    In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. [1] It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions.

  6. 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]

  7. 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.

  8. 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 ...

  9. 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).