A simple proof for the continuity of infinite convolutions of binary random variables

Let Xj, j [greater-or-equal, slanted] 1, be independent random variables taking the values aj [greater-or-equal, slanted] bj with distribution pj = P(Xj = aj) = 1 - P(Xj = bj). Assume that the infinite series U = [Sigma]Xj is (a.s.) convergent. We give a simple proof for Lévy's theorem on the continuity of the distribution function F(x) of U.

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Year of publication:	1989
Authors:	Galambos, Janos ; Kátai, Imre
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 7.1989, 5, p. 369-370
Publisher:	Elsevier
Keywords:	binary random variables convergent infinite convolution continuity of the limiting distribution

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005259244