# Deriving stochastic independence of vector valued Random variables [duplicate]

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.
• 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? – whuber Feb 6 '18 at 19:20
• are you sure that this cannot be proven with the information given? also not if $X_i$ are Unif(0,1) distributed? – Sebastian Feb 6 '18 at 19:33
• Aaah One knows what that $X_{n,j}$ are Independent – Sebastian Feb 6 '18 at 20:42