Probability and Mathematical Statistics: Vol. 9, Fasc. 2


	UNIVERSITY OF WROCŁAW

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	WROCŁAW UNIVERSITY OF SCIENCE AND TECHNOLOGY

Contents of PMS, Vol. 9, Fasc. 2, pages 105 - 111

SOME CHARACTERIZATIONS OF THE EXPONENTIAL DISTRIBUTION FUNCTION Bolesław Kopociński Abstract: Let $X$ be a nonnegative random variable and let $[x]$ denote the integer part of $x.$ The main result of the paper is the following characterization: $X$ $is$ $exponentially$ $distributed$ iff $[aX]$ $and$ $aX - [aX]$ $are$ $mutually$ $independent$ $for$ $every$ $a > 0.$ Some modifications of this theorem are also considered. 2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -; Key words and phrases: -

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