Mothematician Post №2: non-correlation does not imply non-causation

...Or, more rigorously, non-correlation does not imply independence.

As this little guy and everybody else knows, one of the most famous correlation coefficients out there is Pearson's correlation coefficient: cor(ξ, η) = (E[(ξ-E[ξ])(η-E[η])])/sqrt(D[ξ]D[η]), where E[x] is the mathematical expectation of random variable x, D[x] is the dispersion of random variable x, and sqrt(x) is the (prime) square root of x.

As we all know, if cor(ξ, η) != 0, then ξ and η are not independent random variables. But recently, this little guy heard that it does not follow from cor(ξ, η) = 0 that ξ and η are independent. Obviously, he craves the light of knowledge and wants to hear some examples of non-independent random variables having a correlation coefficient of 0.