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...

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

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...

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...

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

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

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...

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...

Kolmogorov's inequality Kunita–Watanabe inequality Le Cam's theorem Lenglart's inequality Marcinkiewicz–Zygmund inequality Markov's inequality McDiarmid's...

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...

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

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

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...

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

{\displaystyle p} with 1 ≤ p < ∞ , {\displaystyle 1\leq p<\infty ,} then by Markov's inequality, λ f ( t ) ≤ ‖ f ‖ p p t p {\displaystyle \lambda _{f}(t)\leq {\frac...

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

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

In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability...

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

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

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

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...

{(X^{2}/K_{2}^{2})}]\leq 2.} ( 2 ) ⟹ ( 1 ) {\displaystyle (2)\implies (1)} By Markov's inequality, P ⁡ ( | X | ≥ t ) = P ⁡ ( exp ⁡ ( X 2 K 2 2 ) ≥ exp ⁡ ( t 2 K 2...

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

mean values that are close, due to the central limit theorem and Markov's inequality. With inadequate randomization or low sample size, the systematic...

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...

systematic way. The first term in F {\displaystyle F} comes from applying Markov's inequality to bound the probability of the first bad event (the cost is too...

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