Probabilistic inequalities

Cantelli's inequality

In probability theory, Cantelli's inequality (also called the Chebyshev-Cantelli inequality and the one-sided Chebyshev inequality) is an improved version of Chebyshev's inequality for one-sided tail bounds. The inequality states that, for where is a real-valued random variable, is the probability measure, is the expected value of , is the variance of . Applying the Cantelli inequality to gives a bound on the lower tail, While the inequality is often attributed to Francesco Paolo Cantelli who published it in 1928, it originates in Chebyshev's work of 1874. When bounding the event random variable deviates from its mean in only one direction (positive or negative), Cantelli's inequality gives an improvement over Chebyshev's inequality. The Chebyshev inequality has "higher moments versions" and "vector versions", and so does the Cantelli inequality. (Wikipedia).

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Carlo Gasbarri: Liouville’s inequality for transcendental points on projective varieties

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From playlist Algebraic and Complex Geometry

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From playlist Solve and Graph Inequalities | Learn About

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From playlist Solve and Graph Inequalities | Learn About

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From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester

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From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"

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From playlist ALGEBRA CH 3 FORMULAS, INEQUALITIES, ABSOLUTE VALUES

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Related pages

Chebyshev's inequality | Variance | Random variable | Expected value | Probability theory | Markov's inequality | Paley–Zygmund inequality | Probability measure