Collineation, covariance - X and Y are independent, then Cov(X, Y ) = 0

Hello,
I am solving a problem with collineation and covariance. One of sentences says:

if X and Y are independent, then Cov(X, Y ) = 0.

this statement is in regular meaning. Do you know some example where this isn't true

Thank you for your response

I'm not sure what you mean by "collineation" but "cov(X, Y)= 0" is pretty much the definition of "X and Y independent". The fact the, say is true does not change the probability that the other is true.

HallsofIvy said:

I'm not sure what you mean by "collineation" but "cov(X, Y)= 0" is pretty much the definition of "X and Y independent". The fact the, say is true does not change the probability that the other is true.

Click to expand...

Almost but not quite (and I know this only because I had to go reading). Example given was Y=X² for which the covariance is zero and dependence is non-linear. The co-variance is a linear measure.

Still need to read some more to comment on problem if I get that far.