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

Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2010)

  • Volume: 18, Issue: 4, page 213-217
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Hiroyuki Okazaki, and Yasunari Shidama. "Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables." Formalized Mathematics 18.4 (2010): 213-217. <http://eudml.org/doc/266994>.

@article{HiroyukiOkazaki2010,
abstract = {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.},
author = {Hiroyuki Okazaki, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {213-217},
title = {Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables},
url = {http://eudml.org/doc/266994},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Hiroyuki Okazaki
AU - Yasunari Shidama
TI - Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 4
SP - 213
EP - 217
AB - 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.
LA - eng
UR - http://eudml.org/doc/266994
ER -

References

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