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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.
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 ...
Such inequalities are of importance in several fields, including communication complexity (e.g., in proofs of the gap Hamming problem [13]) and graph theory. [14] An interesting anti-concentration inequality for weighted sums of independent Rademacher random variables can be obtained using the Paley–Zygmund and the Khintchine inequalities. [15]
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
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 mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if ...
In number theory, Chebyshev's bias is the phenomenon that most of the time, there are more primes of the form 4k + 3 than of the form 4k + 1, up to the same limit. This phenomenon was first observed by Russian mathematician Pafnuty Chebyshev in 1853.