In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some...

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...

X {\displaystyle X} . Chebyshev's inequality can be seen as a special case of the generalized Markov's inequality applied to the random variable | X...

not required by either Markov's inequality or Chebyshev's inequality. The Chernoff bound is related to the Bernstein inequalities. It is also used to prove...

kind. Bernstein's inequality (mathematical analysis) Remez inequality Markov's inequality is used to obtain lower bounds in computational complexity theory...

decision process Markov's inequality Markov brothers' inequality Markov information source Markov network Markov number Markov property Markov process Stochastic...

A Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on...

inequality Etemadi's inequality Landau–Kolmogorov inequality Markov's inequality Bernstein inequalities (probability theory) Billingsley, Patrick (1995)...

n {\displaystyle S_{n}=X_{1}+\cdots +X_{n}} . Then for s, t > 0, Markov's inequality and the independence of Xi implies: P ⁡ ( S n − E [ S n ] ≥ t ) =...

finite expectation, then Markov's inequality may be applied to the random variable |X−E[X]|2 to obtain Chebyshev's inequality P ⁡ ( | X − E [ X ] | ≥ a...

variables having a Markov property described by an undirected graph Markov's inequality, a probabilistic upper bound Markovian (disambiguation) Markovo (disambiguation)...

Chebyshev–Markov–Stieltjes inequalities Chebyshev's sum inequality Clarkson's inequalities Eilenberg's inequality Fekete–Szegő inequality Fenchel's inequality Friedrichs's...

{\frac {\operatorname {E} [X_{0}]}{a}}\ .} The inequality is a generalization of Markov's inequality. Ville, Jean (1939). Etude Critique de la Notion...

inequality Markov's inequality Minkowski inequality Nesbitt's inequality Pedoe's inequality Poincaré inequality Samuelson's inequality Sobolev inequality Triangle...

chain algorithm Markov partition Markov property Markov odometer Markov perfect equilibrium (game theory) Markov's inequality Markov spectrum in Diophantine...

In mathematical analysis, the Chebyshev–Markov–Stieltjes inequalities are inequalities related to the problem of moments that were formulated in the 1880s...

contradiction. Common tools used in the probabilistic method include Markov's inequality, the Chernoff bound, and the Lovász local lemma. Although others...

The moment-generating function can be used in conjunction with Markov's inequality to bound the upper tail of a real random variable X. This statement...

Markov's inequality Chebyshev's inequality = Chernoff bound Chernoff's inequality Bernstein inequalities (probability theory) Hoeffding's inequality Kolmogorov's...

|f(x)|^{p}} . This representation can be used to prove Markov's inequality and Chebyshev's inequality. Symmetric decreasing rearrangement Willem, Michel (2013)...

in Fan et al. (2015). The proofs are based on an application of Markov's inequality to the random variable exp ⁡ ( λ ∑ j = 1 n X j ) , {\displaystyle...

the inequality ‖ f ‖ 1 , w ≤ ‖ f ‖ 1 . {\displaystyle \|f\|_{1,w}\leq \|f\|_{1}.} This is nothing but Markov's inequality (aka Chebyshev's Inequality)....

Lagrange's theorem (number theory) Liouville's theorem (complex analysis) Markov's inequality (proof of a generalization) Mean value theorem Multivariate normal...

\alpha \right]\leq {\frac {a(n,k,X(\Omega ))}{\alpha }}} using the Markov's inequality and the expectation derived previously. Similarly, show that ∀ α...

first moment. The first moment method is a simple application of Markov's inequality for integer-valued variables. For a non-negative, integer-valued...

=\operatorname {P} (A).} This identity is used in a simple proof of Markov's inequality. In many cases, such as order theory, the inverse of the indicator...

Chernoff bound Gauss's inequality Markov's inequality Rule of succession Rule of three (medicine) Vysochanskiï–Petunin inequality Chi-squared test Diagnostic...

\sum _{s}c(s)\lambda x_{s}^{*}=\lambda c\cdot x^{*}} . Thus, by Markov's inequality, the probability of the first bad event above is at most 1 / 2 {\displaystyle...

a non-negative continuous random variable having an expectation, Markov's inequality states that F ¯ X ( x ) ≤ E ⁡ ( X ) x . {\displaystyle {\bar {F}}_{X}(x)\leq...

The region of interest for which Markov's inequality gives a lower bound....