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Chebyshev's inequality then follows by dividing by k 2 σ 2. This proof also shows why the bounds are quite loose in typical cases: the conditional expectation on the event where | X − μ | < kσ is thrown away, and the lower bound of k 2 σ 2 on the event | X − μ | ≥ kσ can be quite poor.
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 ...
In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if ...
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).
the most common choice for function h being either the absolute value (in which case it is known as Markov inequality), or the quadratic function (respectively Chebyshev's inequality). Another useful result is the continuous mapping theorem : if T n is consistent for θ and g (·) is a real-valued function continuous at point θ , then g ( T n ...
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.
WASHINGTON (Reuters) -President-elect Donald Trump said on Saturday the U.S. should not be involved in the conflict in Syria, where rebel forces are threatening the government of President Bashar ...
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 ...