Skip to main content

Computational Formulas

  • Chapter
  • First Online:
Mathematical Theory of Democracy

Part of the book series: Studies in Choice and Welfare ((WELFARE))

  • 1630 Accesses

Abstract

Chebyshev’s inequality [Korn and Korn 1968, 18.3.5].For a random variable X with expectation\( \mu \) and variance \( \sigma^2 \) it holds :

$$\mathrm{Pr}(|X-\mu|\geq C)\;\leq\; \frac{\sigma^2}{C^2}\qquad(C\;>\;0) $$

Men who wish to know about the world must learn about it in its particular details.

Heraclitus (535–475? BC)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramowitz M, Stegun I (1972) Handbook ofmathematical functions. Dover, New York

    Google Scholar 

  2. Beta distribution (2013).Wikipedia.http://en.wikipedia.org/wiki/Beta distribution. Cited 6 Apr 2013

  3. Central limit theorem (2013).Wikipedia.http://en.wikipedia.org/wiki/Central limit theorem. Cited 6 Apr 2013

  4. Chebyshev’s inequality (2013).Wikipedia.http://en.wikipedia.org/wiki/Chebyshev’s inequality. Cited 14 Apr 2013

  5. Graham RL, Knuth DE, Patashnik O (1988) Concrete mathematics.Addison-Wesley, Reading MA

    Google Scholar 

  6. Feller W (1968) An introduction to probability theory and its applications.3rd ed. Wiley, New York

    Google Scholar 

  7. Korn GA, Korn ThM (1968) Mathematical handbook forscientists and engineers. McGrow-Hill, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Tangian, A. (2014). Computational Formulas. In: Mathematical Theory of Democracy. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38724-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38724-1_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38723-4

  • Online ISBN: 978-3-642-38724-1

  • eBook Packages: Business and EconomicsEconomics and Finance (R0)

Publish with us

Policies and ethics