I just have a question concerning the definition of independent random vectors.
The random vectors $X=[X_1, \ldots, X_n]$ and $Y=[Y_1,\ldots, Y_m]$ are independent means that $X_1,...,X_n,Y_1,...,Y_m$ are independent random variables?
2026-03-27 17:52:35.1774633955
About the definition of independent random vectors
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No. For example $(X,X)$ and $(Y,Y)$ are independent if $X$ and $Y$ are independent. There is no need for the components inside each vector to be independent.