Quick simple question

Hi to all,



I have the following quick and simple question, and was wondering whether someone could confirm:



Let <X11,X12,...,X1n> and <X21,X22,...,X2m> be two random vectors.

Assume that these two vectors are "statistically independent". Does this mean that X1avg=(X11+...+X1n)/n and X2avg=(X21+...+X2m)/m are two independent random variables?



Thanks

Quick simple question