# Making two dependent random variables independent.

This might be a naive question, but suppose I have two random variables f and g that are dependent, and I have a third random variables k that is independent of both. When can I say that f and g + k are independent random variables? If that's not true, then what is one way to turn two dependent variables into independent ones (by some non-trivial operation on one of them, say)?

• Intuitively, I think it's unlikely for $f$ and $g+k$ to be independent (if we're talking real-valued random variables), since the value of $f$ influences the value of $g$ and hence the maximum (say) value of $g+k$. For example, take $f\in\{-1,1\}$ with equal probability, take $g=f$, and take $k$ uniformly distributed on $(-1,1)$. One might be able to cook up exceptions, though. – Greg Martin Nov 19 '13 at 4:45