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Probability pp 131-307 | Cite as

Mathematical Foundations of Probability Theory

  • A. N. Shiryaev
Part of the Graduate Texts in Mathematics book series (GTM, volume 95)

Abstract

The models introduced in the preceding chapter enabled us to give a probabilistic-statistical description of experiments with a finite number of outcomes. For example, the triple (Ω, A, P) with
$$\Omega = \left\{ {\omega :\omega = \left( {{a_1},...,{a_n}} \right),{a_i} = 0,1} \right\},A = \left( {A:A \subseteq \Omega } \right)$$
and \(p\left( \omega \right) = {p^{\sum {{a_i}} }}{q^{n - \sum {{a_i}} }} \) is a model for the experiment in which a coin is tossed n times “independently” with probability p of falling head. In this model the number N(Ω) of outcomes, i.e. the number of points in Ω, is the finite number 2 n .

Keywords

Probability Measure Measurable Space Conditional Expectation Random Element Mathematical Foundation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • A. N. Shiryaev
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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