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Let $(X_{n}), n= 1,...4$ independent real valued random variables. Are $(X_1,X_2)$ and $(X_3,X_4)$ independent? If so please prove why.

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marked as duplicate by whuber Feb 6 '18 at 20:49

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  • $\begingroup$ You cannot prove this with the information given. Are you also assuming the $(\mathbf{X}_n)$ are independent where $\mathbf{X}_n = (X_{n,1}, \ldots, X_{n,r})$? If that's the case, your question is asked and answered at stats.stackexchange.com/questions/94872. If it's not the case, then what are you assuming? $\endgroup$ – whuber Feb 6 '18 at 19:20
  • $\begingroup$ no i do not assume this. $\endgroup$ – Sebastian Feb 6 '18 at 19:24
  • $\begingroup$ are you sure that this cannot be proven with the information given? also not if $X_i$ are Unif(0,1) distributed? $\endgroup$ – Sebastian Feb 6 '18 at 19:33
  • $\begingroup$ How could you possibly conclude that a set of variables is independent if you know absolutely nothing about them? $\endgroup$ – whuber Feb 6 '18 at 20:40
  • $\begingroup$ Aaah One knows what that $X_{n,j} $ are Independent $\endgroup$ – Sebastian Feb 6 '18 at 20:42

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