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Let $U_1,U_2,\ldots,U_n$ be $n\geq 2$ mutually independent Bernoulli random variables. There are two cases of interest: $1.$ The random variables $U_1,U_2,\ldots,U_n$ are identically distributed; $...

I would like to know whether the following problem is well posed, and whether there is a solution. Let me make it clear that I have no pretentions of rigor here. Given a continuum random variable $x$...