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By comparison, Chebyshev's inequality states that all but a 1/N fraction of the sample will lie within √ N standard deviations of the mean. Since there are N samples, this means that no samples will lie outside √ N standard deviations of the mean, which is worse than Samuelson's inequality.
Let P 0,P 1, ...,P m be the first m + 1 orthogonal polynomials [clarification needed] with respect to μ ∈ C, and let ξ 1,...ξ m be the zeros of P m. It is not hard to see that the polynomials P 0 , P 1 , ..., P m -1 and the numbers ξ 1 ,... ξ m are the same for every μ ∈ C , and therefore are determined uniquely by m 0 ,..., m 2 m -1 .
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.
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 ...
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
In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if ...
Graph of number of coupons, n vs the expected number of trials (i.e., time) needed to collect them all E (T ) In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests.
While the inequality is often attributed to Francesco Paolo Cantelli who published it in 1928, [4] it originates in Chebyshev's work of 1874. [5] When bounding the event random variable deviates from its mean in only one direction (positive or negative), Cantelli's inequality gives an improvement over Chebyshev's inequality. The Chebyshev ...