The definition of independence of random variables from a measure-theoretic standpoint is so confusing (independence of generated sigma-algebras, etc.) that I cannot answer this seemingly simple question...So if [itex]X,Y[/itex] are independent random variables, does that mean [itex]X,X^2,X^3,X^4,\ldots[/itex] and [itex]Y,Y^2,Y^3,\ldots[/itex] are each pairwise independent?(adsbygoogle = window.adsbygoogle || []).push({});

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# If X and Y are independent, are X^k and Y?

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