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.
@article{bwmeta1.element.doi-10_2478_v10037-010-0026-6,
author = {Hiroyuki Okazaki and Yasunari Shidama},
title = {Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables},
journal = {Formalized Mathematics},
volume = {18},
year = {2010},
pages = {213-217},
zbl = {1281.60006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0026-6}
}
Hiroyuki Okazaki; Yasunari Shidama. Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables. Formalized Mathematics, Tome 18 (2010) pp. 213-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0026-6/
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