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Formalized Mathematics

(a computer assisted approach)

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Volume 18, Issue 4 (Jan 2010)

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Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables

Hiroyuki Okazaki
  • Shinshu University, Nagano, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2011-01-05 | DOI: https://doi.org/10.2478/v10037-010-0026-6

Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables

In this article we continue formalizing probability and randomness started in [13], where we formalized some theorems concerning the probability and real-valued random variables. In this paper we formalize the variance of a random variable and prove Chebyshev's inequality. Next we formalize the product probability measure on the Cartesian product of discrete spaces. In the final part of this article we define the algebra of real-valued random variables.

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About the article


Published Online: 2011-01-05

Published in Print: 2010-01-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-010-0026-6. Export Citation

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