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Suppose that a distribution F is given. Does there always exist a sequence of independent random variables following F? Moreover, given two distributions F and G and a random variable X following F, does there exist a random variable Y following G, such that X and Y are independent?

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    I don't understand the phrase "independent random variables following F" even after a search. Would you define it?2012-10-18
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    @Ross Millikan I am sure the OP means "independent random variables having same CDF $F$"2012-10-18

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