A Characterization of Uniform Distribution

• Autorzy: Joanna Chachulska
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 62E10: Characterization and structure theory
• 28A12: Contents, measures, outer measures, capacities
• 60E05: Distributions: general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: 53
• Numer: 2
• Strony: 207-220

Daty

wydano

2005

Twórcy

autor

Joanna Chachulska

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba53-2-9