CHARACTERIZATION OF GEOMETRIC AND EXPONENTIAL DISTRIBUTIONS.
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
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In two works T. S. Ferguson examines the classes of independent random variables X and Y such that minX,Y is independent of X - Y. In one work he shows that if X or Y has a discrete part, then X and Y are geometric random variables. In the other work it is shown that if X and Y are absolutely continuous, then they are exponential random variables. The present author intends to complete this investigation by showing that the result of Ferguson holds even if X and Y are possibly singular.