Search results
Results From The WOW.Com Content Network
Borel's law of large numbers, ... It is a special case of any of several more general laws of large numbers in probability theory. Chebyshev's inequality.
The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics. The inequality has great utility because it can be applied to any probability distribution in which the mean and variance are defined. For example, it can be used to prove the weak law of large numbers.
The Chebyshev inequality is used to prove the weak law of large numbers. [ citation needed ] The Bertrand–Chebyshev theorem (1845, 1852) states that for any n > 3 {\displaystyle n>3} , there exists a prime number p {\displaystyle p} such that n < p < 2 n {\displaystyle n<p<2n} .
Another almost universal example of a secondary random variable is the law of large numbers of classical probability theory which states that sums of independent random variables, under mild conditions, concentrate around their expectation with a high probability.
Chebyshev's inequality = Chernoff bound; Chernoff's inequality; Bernstein inequalities (probability theory) Hoeffding's inequality; Kolmogorov's inequality; Etemadi's inequality; Chung–Erdős inequality; Khintchine inequality; Paley–Zygmund inequality; Laws of large numbers. Asymptotic equipartition property; Typical set; Law of large numbers
Bienaymé criticized Poisson's "law of large numbers" and was involved in a controversy with Augustin Louis Cauchy. Both Bienaymé and Cauchy published regression methods at about the same time. Bienaymé had generalized the method of ordinary least squares. The dispute within the literature was over the superiority of one method over the other.
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 ...