Abstract
The function F(x), x ∈ ℝ1, is called a distribution function (d.f.) if:
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(a)
F is a non-decreasing function; i.e., F(x1) ⩽ F(x2) if x1 < x2;
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(b)
F is a left-continuous function; i.e., F(x - 0) = F(x), x ∈ ℝ1;
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(c)
$$ \lim \mathop {}\limits_{x \to \infty } F(X) = 1,{\mkern 1mu} \lim \mathop {}\limits_{x \to - \infty {\mkern 1mu} } F(X) = 0 $$
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© 1989 Kluwer Academic Publishers
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Stoyanov, J., Mirazchiiski, I., Ignatov, Z., Tanushev, M. (1989). Characteristics of Random Variables. In: Exercise Manual in Probability Theory. Mathematics and Its Applications, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2927-2_3
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DOI: https://doi.org/10.1007/978-94-009-2927-2_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7818-4
Online ISBN: 978-94-009-2927-2
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