Abstract
It has occurred to us that our lives are deluged by facts and figures from technical, business and sports reports. No doubt that some of these facts are curious enough or can even shake our imagination. However, this information is of real use if we can build a mathematical model allowing us to highlight the real phenomena and revealing the governing laws hidden initially under the informational avalanche. In many models, random factors have come to play an important role. Such models are called probabilistic. They are described in terms of the following basic concepts which are assumed familiar to readers:
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(i)
a random variable (r.v.) X;
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(ii)
the distribution function (d.f.) F(x) = P(X ≤ x) of r.v. X;
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(iii)
the expectation E X of r.v. X;
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(iv)
the independence of r.v.’s;
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(v)
the total probability formula;
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(vi)
the conditional distribution;
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(vii)
the Markov chain.
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Commentaries
Section 1
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Kalashnikov, V. (1997). Introduction. In: Geometric Sums: Bounds for Rare Events with Applications. Mathematics and Its Applications, vol 413. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1693-2_1
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DOI: https://doi.org/10.1007/978-94-017-1693-2_1
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