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A Characterization of Uniform Distribution

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Chachulska J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

tom 53

nr 2

207-220

Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous or discrete. No assumptions are imposed on the supports of the distributions of X and Y.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Chachulska J.

1 2005

Wyniki wyszukiwania

A Characterization of Uniform Distribution