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

Open access

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.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics 1(1):107-114 1990.

  • [2] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics 2(1):173-183 1991.

  • [3] Czesław Byliński. Binary operations. Formalized Mathematics 1(1):175-180 1990.

  • [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics 1(1):55-65 1990.

  • [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics 1(1):153-164 1990.

  • [6] Czesław Byliński. Partial functions. Formalized Mathematics 1(2):357-367 1990.

  • [7] Czesław Byliński. Some basic properties of sets. Formalized Mathematics 1(1):47-53 1990.

  • [8] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics 1(4):661-668 1990.

  • [9] Agata Darmochwał. Finite sets. Formalized Mathematics 1(1):165-167 1990.

  • [10] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics 1(2):269-272 1990.

  • [11] Keiko Narita Noboru Endou and Yasunari Shidama. Integral of complex-valued measurable function. Formalized Mathematics 16(4):319-324 2008 doi:10.2478/v10037-008-0039-6.

  • [12] Andrzej Nędzusiak. s-fields and probability. Formalized Mathematics 1(2):401-407 1990.

  • [13] Hiroyuki Okazaki and Yasunari Shidama. Probability on finite set and real-valued random variables. Formalized Mathematics 17(2):129-136 2009 doi: 10.2478/v10037-009-0014-x.

  • [14] Henryk Oryszczyszyn and Krzysztof Prażmowski. Real functions spaces. Formalized Mathematics 1(3):555-561 1990.

  • [15] Yasunari Shidama and Noboru Endou. Integral of real-valued measurable function. Formalized Mathematics 14(4):143-152 2006 doi:10.2478/v10037-006-0018-8.

  • [16] Yasunari Shidama Hikofumi Suzuki and Noboru Endou. Banach algebra of bounded functionals. Formalized Mathematics 16(2):115-122 2008 doi:10.2478/v10037-008-0017-z.

  • [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics 1(2):329-334 1990.

  • [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics 1(1):67-71 1990.

  • [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics 1(1):73-83 1990.

  • [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics 1(1):181-186 1990.

  • [21] Hiroshi Yamazaki Yasunari Shidama and Yatsuka Nakamura. Bessel's inequality. Formalized Mathematics 11(2):169-173 2003.

  • [22] Bo Zhang Hiroshi Yamazaki and Yatsuka Nakamura. The relevance of measure and probability and definition of completeness of probability. Formalized Mathematics 14(4):225-229 2006 doi:10.2478/v10037-006-0026-8.

Search
Journal information
Impact Factor


CiteScore 2018: 0.42

SCImago Journal Rank (SJR) 2018: 0.111
Source Normalized Impact per Paper (SNIP) 2018: 0.169

Target audience:

researchers in the fields of formal methods and computer-checked mathematics

Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 206 127 2
PDF Downloads 51 30 0