• 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...
    14 KB (2,521 words) - 05:23, 13 December 2024
  • kind. Bernstein's inequality (mathematical analysis) Remez inequality Markov's inequality is used to obtain lower bounds in computational complexity theory...
    2 KB (306 words) - 03:09, 20 April 2025
  • 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...
    53 KB (8,288 words) - 15:32, 6 July 2025
  • 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...
    32 KB (5,093 words) - 19:36, 24 June 2025
  • chain algorithm Markov partition Markov property Markov odometer Markov perfect equilibrium (game theory) Markov's inequality Markov spectrum in Diophantine...
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  • Thumbnail for Andrey Markov
    decision process Markov's inequality Markov brothers' inequality Markov information source Markov network Markov number Markov property Markov process Stochastic...
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  • 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...
    18 KB (3,160 words) - 13:04, 14 May 2025
  • 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 ) =...
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    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...
    52 KB (7,622 words) - 16:58, 25 June 2025
  • Kolmogorov's inequality Kunita–Watanabe inequality Le Cam's theorem Lenglart's inequality Marcinkiewicz–Zygmund inequality Markov's inequality McDiarmid's...
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  • 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...
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  • inequality Etemadi's inequality Landau–Kolmogorov inequality Markov's inequality Bernstein inequalities (probability theory) Billingsley, Patrick (1995)...
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  • Thumbnail for Inequality (mathematics)
    inequality Markov's inequality Minkowski inequality Nesbitt's inequality Pedoe's inequality Poincaré inequality Samuelson's inequality Sobolev inequality Triangle...
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  • Thumbnail for Cumulative distribution function
    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...
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  • contradiction. Common tools used in the probabilistic method include Markov's inequality, the Chernoff bound, and the Lovász local lemma. Although others...
    12 KB (1,957 words) - 01:18, 19 May 2025
  • {\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...
    65 KB (12,204 words) - 16:12, 8 July 2025
  • variables having a Markov property described by an undirected graph Markov's inequality, a probabilistic upper bound Markovian (disambiguation) Markovo (disambiguation)...
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  • \alpha \right]\leq {\frac {a(n,k,X(\Omega ))}{\alpha }}} using the Markov's inequality and the expectation derived previously. Similarly, show that ∀ α...
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  • Thumbnail for Markov chain
    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...
    96 KB (12,900 words) - 19:30, 30 June 2025
  • {\frac {\operatorname {E} [X_{0}]}{a}}\ .} The inequality is a generalization of Markov's inequality. Ville, Jean (1939). Etude Critique de la Notion...
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  • Chernoff bound Gauss's inequality Markov's inequality Rule of succession Rule of three (medicine) Vysochanskiï–Petunin inequality Chi-squared test Diagnostic...
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  • Markov's inequality Chebyshev's inequality = Chernoff bound Chernoff's inequality Bernstein inequalities (probability theory) Hoeffding's inequality Kolmogorov's...
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  • 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...
    19 KB (2,820 words) - 11:49, 25 April 2025
  • {(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...
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  • Second moment method (category Probabilistic inequalities)
    first moment. The first moment method is a simple application of Markov's inequality for integer-valued variables. For a non-negative, integer-valued...
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  • mean values that are close, due to the central limit theorem and Markov's inequality. With inadequate randomization or low sample size, the systematic...
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  • 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)....
    9 KB (1,488 words) - 16:48, 27 March 2025
  • Lagrange's theorem (number theory) Liouville's theorem (complex analysis) Markov's inequality (proof of a generalization) Mean value theorem Multivariate normal...
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  • 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...
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    |f(x)|^{p}} . This representation can be used to prove Markov's inequality and Chebyshev's inequality. Symmetric decreasing rearrangement Willem, Michel (2013)...
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