A Note on Chebyshev Inequality: To Explain or to Predict

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Amaresh Das
Amaresh Das
α University of New Orleans University of New Orleans

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A Note on Chebyshev Inequality: To Explain or to Predict

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Abstract

The question is: What proportion of the total probability of a random varriable X lies within a certain interval of the mea 𝜇𝜇? What is the probability of being hit by a meteor greater in size than five times the standard deviation above the mean? Because it can be applied to completely arbitrary distributions(unknown except for mean and variables), the inequality generally gives a poor bound compared to what might be deduced if more aspects are known about the distribution involved.

References

5 Cites in Article
  1. Anirban Dasgupta (2000). Best constants in Chebyshev inequalities with various applications.
  2. K Ferentinos (1982). On Tcebycheff's type inequalities.
  3. Samuel Kotz,N Balakrishnan,Norman Johnson (2012). Continuous Multivariate Distributions.
  4. D Lal (1955). A Note on a Form of Tchebusheff's Inequality Two or More Variables.
  5. M Mood,Grayhill (1963). A.M. Mood and F.A. Graybill Introduction to the Theory of Statistics. Second Edition. McGraw-Hill Series in Probability and Statistics. New York, San Francisco, Toronto, London, McGraw-Hill Book Company, Inc., 1963, XV p. 443 p., 69/6..

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Amaresh Das. 2017. \u201cA Note on Chebyshev Inequality: To Explain or to Predict\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 17 (GJSFR Volume 17 Issue F5): .

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Issue Cover
GJSFR Volume 17 Issue F5
Pg. 25- 29
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Classification
GJSFR-F Classification: MSC 2010: 11Y16
Version of record

v1.2

Issue date

August 24, 2017

Language
en
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The question is: What proportion of the total probability of a random varriable X lies within a certain interval of the mea 𝜇𝜇? What is the probability of being hit by a meteor greater in size than five times the standard deviation above the mean? Because it can be applied to completely arbitrary distributions(unknown except for mean and variables), the inequality generally gives a poor bound compared to what might be deduced if more aspects are known about the distribution involved.

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A Note on Chebyshev Inequality: To Explain or to Predict

Amaresh Das
Amaresh Das University of New Orleans

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