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In the second chapter, random variables are introduced and investigated in the framework of axiomatic of Kolmogorov. It is shown a connection of probability distributions and distributions of random variables as well as their distribution functions. The notion of the Lebesgue integral is given in context of definition of moments of random variables (see Baldi, An introduction through theory and exercises, 2017; Çinlar, Probability and stochastics, 2011; Durrett, Essentials of stochastic processes, 2018; Jacod and Protter, Probability essentials, 2003; Kolmogorov, Foundations of the theory of probability, 1956; Krylov, Introduction to the theory of random processes, 2002; Shiryaev, Probability, 1996, and Williams, Probability and martingales, 1991).

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Random Variables and Their Quantitative Characteristics

  • 章节

  • 发表日期：

    2026年

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  • Alexander Melnikov

摘要

In the second chapter, random variables are introduced and investigated in the framework of axiomatic of Kolmogorov. It is shown a connection of probability distributions and distributions of random variables as well as their distribution functions. The notion of the Lebesgue integral is given in context of definition of moments of random variables (see Baldi, An introduction through theory and exercises, 2017; Çinlar, Probability and stochastics, 2011; Durrett, Essentials of stochastic processes, 2018; Jacod and Protter, Probability essentials, 2003; Kolmogorov, Foundations of the theory of probability, 1956; Krylov, Introduction to the theory of random processes, 2002; Shiryaev, Probability, 1996, and Williams, Probability and martingales, 1991).