Characterization problems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions in these variables. One famous example of a characterization problem is the classical Kac-Bernstein theorem: if for two independent random variables ξ_1 and ξ_2, ξ_1 + ξ_2 und ξ_1 - ξ_2 are independent then ξ_1 and ξ_2 are Gaussian random variables.
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