Articles containing proofs | Probabilistic inequalities | Statistical inequalities

Chebyshev's inequality

In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1/k2 of the distribution's values can be k or more standard deviations away from the mean (or equivalently, at least 1 − 1/k2 of the distribution's values are less than k standard deviations away from the mean). The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics. The inequality has great utility because it can be applied to any probability distribution in which the mean and variance are defined. For example, it can be used to prove the weak law of large numbers. Its practical usage is similar to the 68–95–99.7 rule, which applies only to normal distributions. Chebyshev's inequality is more general, stating that a minimum of just 75% of values must lie within two standard deviations of the mean and 88.89% within three standard deviations for a broad range of different probability distributions. The term Chebyshev's 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 inequality as "Chebyshev's First Inequality," and the similar one referred to on this page as "Chebyshev's Second Inequality." (Wikipedia).

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Chebyshev's inequality

In this video, I state and prove Chebyshev's inequality, and its cousin Markov's inequality. Those inequalities tell us how big an integrable function can really be. Enjoy!

From playlist Real Analysis

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Statistics - How to use Chebyshev's Theorem

In this video I cover at little bit of what Chebyshev's theorem says, and how to use it. Remember that Chebyshev's theorem can be used with any distribution, and that it gives a lower proportion of what we can expect in the actual data. ▬▬ Chapters ▬▬▬▬▬▬▬▬▬▬▬ 0:00 Start 0:04 What is C

From playlist Statistics

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Probability: Chebyshev's Inequality Proof & Example

Today, we prove Chebyshev's inequality and give an example.

From playlist Probability

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CHEBYSHEV’S Theorem: An Inequality for Everyone (6-7)

Chebyshev’s Theorem (or Chebyshev’s Inequality) states that at least 1- (1/z2) of the items in any data set will be within z standard deviations of the mean, where z is any value greater than 1 and z need not be an integer. At least 75% of the data values must be within z = 2 standard dev

From playlist Depicting Distributions from Boxplots to z-Scores (WK 6 QBA 237)

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How to solve Chebyshev's equation

I show how to solve Chebyshev's differential equation via an amazing substitution. The substitution results in forming a new differential equation with constant coefficients.

From playlist Differential equations

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Chebyshev's Theorem

This statistics video tutorial provides a basic introduction into Chebyshev's theorem which states that the minimum percentage of distribution values that lie within k standard deviations of the mean is equal to 1 - 1/K^2. How To Calculate Federal Income Taxes: https://www.youtube.com/wat

From playlist Statistics

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Algebra - Ch. 31: Linear Inequality in 2 Variables (2 of 14) Differences

Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between “greater-than or equalto” and “greater-than”, and “less-than or equal to” and “less-than” graphi

From playlist ALGEBRA CH 31 LINEAR INEQUALITIES IN 2 VARIABLES

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Chebyshev's Theorem

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Chebyshev's Theorem - In this video, I state Chebyshev's Theorem and use it in a 'real life' problem.

From playlist All Videos - Part 4

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Probabilty Bounds

MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 View the complete course: http://ocw.mit.edu/6-041SCF13 Instructor: Kuang Xu License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013

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L18.8 Related Topics

MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

From playlist MIT RES.6-012 Introduction to Probability, Spring 2018

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12/05/2019, Nicolas Brisebarre

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From playlist Fall 2019 Symbolic-Numeric Computing Seminar

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Ramon van Handel: The mysterious extremals of the Alexandrov-Fenchel inequality

The Alexandrov-Fenchel inequality is a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes. It is one of the central results in convex geometry, and has deep connections with other areas of mathematics. The characterization of its extremal bodie

From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability

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19. Weak Law of Large Numbers

MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010 View the complete course: http://ocw.mit.edu/6-041F10 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013

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Convergence in Probability and in the Mean Part 1

MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 View the complete course: http://ocw.mit.edu/6-041SCF13 Instructor: Kuang Xu License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013

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CTNT 2020 - Sieves (by Brandon Alberts) - Lecture 3

The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/

From playlist CTNT 2020 - Sieves (by Brandon Alberts)

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Weird notions of "distance" || Intro to Metric Spaces

Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Weird, fun

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Triangle Inequality Theorem

This video states and investigates the triangle inequality theorem. Complete Video List: http://www.mathispower4u.yolasite.com

From playlist Relationships with Triangles

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68–95–99.7 rule | Samuelson's inequality | Absolute value | Extended real number line | Skewness | Deviation risk measure | Eaton's inequality | Paley–Zygmund inequality | Kolmogorov's inequality | Semidefinite programming | Exchangeable random variables | Method of moments (probability theory) | Standard score | Multivariate random variable | Covariance matrix | Dimension | Median | Hermite–Hadamard inequality | Pareto distribution | Cantelli's inequality | Multidimensional Chebyshev's inequality | Mizar system | Cornish–Fisher expansion | Jensen's inequality | Le Cam's theorem | Pafnuty Chebyshev | Variance | Function (mathematics) | Markov's inequality | Real number | Chebyshev–Markov–Stieltjes inequalities | Probability distribution | Measurable function | Normal distribution | Standard deviation | Mahalanobis distance | Random variable | Expected value | Transpose | Measure space | Probability theory | Logarithmically concave function | Kurtosis | Concentration inequality | Conditional expectation | Chebyshev's sum inequality