Search results
Results from the WOW.Com Content Network
[1] [2] The term Chebyshev's inequality may also refer to Markov's inequality, especially in the context of analysis. They are closely related, and some authors refer to Markov's inequality as "Chebyshev's First Inequality," and the similar one referred to on this page as "Chebyshev's Second Inequality."
1 Solution. Toggle Solution subsection ... Bound the desired probability using the Chebyshev inequality: ... (1995), "8.4 The coupon collector's problem solved", The ...
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).
Chebyshev's equation is the second order linear differential equation + = where p is a real (or complex) constant. The equation is named after Russian mathematician Pafnuty Chebyshev. The solutions can be obtained by power series:
In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if ...
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 ...
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]
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.