Abstract
The concepts of random sampling and statistics of random variables are introduced. We consider estimators of probability characteristics and moments. We discuss the types of convergence used in probability theory, in particular the convergence of a sequence of random variables in probability and convergence in distribution. The law of large numbers and the central limit theorem are described in the classical interpretation. We discuss the statistics of stochastic processes and specific features of samples of random variables and stochastic processes.
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Notes
- 1.
The issue of accuracy is discussed in the next chapter.
- 2.
The following determinations of the sample moments are not the only ones possible.
- 3.
This hypothesis is widely used in metrology for measurement of various physical quantities.
References
Bernoulli, J.: O Zakone Bolshikh Chisel (On the Law of Large Numbers). Nauka, Moskow (1986)
Gnedenko, B.V.: Kurs Teorii Veroyatnostey (Course on Probability Theory). Izdatelstvo physico–matematicheskoj literaturi, Moscow (1988)
Gorban, I.I.: Teoriya Ymovirnostey i Matematychna Statystika dla Naukovykh Pratsivnykiv ta Inzheneriv (Probability Theory and Mathematical Statistics for Scientists and Engineers). IMMSP, NAS of Ukraine, Kiev (2003)
Gorban, I.I.: Sluchaynost i gipersluchaynost (Randomness and Hyper-randomness). Naukova Dumka, Kiev (2016)
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Gorban, I.I. (2018). Fundamentals of the Mathematical Statistics of Probability Theory. In: Randomness and Hyper-randomness. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-60780-1_4
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DOI: https://doi.org/10.1007/978-3-319-60780-1_4
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