So I know that the statement "If two random variables are independent, then the two random variables are uncorrelated" is true.
Does that mean its contraposition "If two random variables are correlated, then the two random variables are dependent." also true?
In terms of the theory of logic, the contrapositive statement should also be true, but then again, I learned "correlation does not imply causation". So I'm a bit confused.
Can someone clarify this? Is the contrapositive statement really true? If so, what is the difference between that statement and the statement "correlation does not imply causation"??
I think the preferred term is generally "not independent" rather than "dependent" for exactly this reason. The term "dependent" might make it sound like there is a causal relation between the two random variables, but "independence" just means that knowing one gives no extra information about the other, so "not independent" means that knowing one does give some information about the other.