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PROBABILITY
AND
MATHEMATICAL STATISTICS
Vol. 9, Fasc. 2 (1988), pp. 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 [αX] and αX − [αX] are mutually independent
f or every α > 0. Some modifications of this theorem are also considered.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -
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