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
Chernoff bound (redirect from Chernoff's inequality)
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...
2 KB (229 words) - 07:10, 17 June 2024
decision process Markov's inequality Markov brothers' inequality Markov information source Markov network Markov number Markov property Markov process Stochastic...
10 KB (1,072 words) - 21:36, 10 June 2025
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 ) =...
13 KB (2,527 words) - 00:07, 27 May 2025
Expected value (section Inequalities)
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...
9 KB (709 words) - 21:10, 14 April 2025
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...
7 KB (1,399 words) - 01:12, 15 January 2025
inequality Etemadi's inequality Landau–Kolmogorov inequality Markov's inequality Bernstein inequalities (probability theory) Billingsley, Patrick (1995)...
4 KB (802 words) - 06:54, 29 January 2025
inequality Markov's inequality Minkowski inequality Nesbitt's inequality Pedoe's inequality Poincaré inequality Samuelson's inequality Sobolev inequality Triangle...
27 KB (3,343 words) - 18:45, 10 May 2025
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...
26 KB (4,110 words) - 15:38, 29 June 2025
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
Lp space (section Hölder's inequality)
{\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)...
5 KB (584 words) - 18:42, 18 May 2025
\alpha \right]\leq {\frac {a(n,k,X(\Omega ))}{\alpha }}} using the Markov's inequality and the expectation derived previously. Similarly, show that ∀ α...
23 KB (3,965 words) - 19:27, 6 July 2025
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...
2 KB (187 words) - 03:45, 13 March 2024
Chernoff bound Gauss's inequality Markov's inequality Rule of succession Rule of three (medicine) Vysochanskiï–Petunin inequality Chi-squared test Diagnostic...
3 KB (279 words) - 13:03, 9 April 2024
Markov's inequality Chebyshev's inequality = Chernoff bound Chernoff's inequality Bernstein inequalities (probability theory) Hoeffding's inequality Kolmogorov's...
11 KB (1,000 words) - 14:07, 2 May 2024
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...
37 KB (7,383 words) - 23:53, 26 May 2025
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...
10 KB (1,690 words) - 21:10, 14 April 2025
mean values that are close, due to the central limit theorem and Markov's inequality. With inadequate randomization or low sample size, the systematic...
36 KB (4,606 words) - 12:37, 20 June 2025
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...
6 KB (593 words) - 20:11, 5 June 2023
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...
24 KB (4,052 words) - 03:12, 2 December 2023
|f(x)|^{p}} . This representation can be used to prove Markov's inequality and Chebyshev's inequality. Symmetric decreasing rearrangement Willem, Michel (2013)...
4 KB (730 words) - 15:32, 20 June 2025