How to prove or disprove the following statement? How to prove or disprove the following statement:
"If random variables X and Y are independent, AND if random variables Y and Z are independent, then X and Z are independent."
I tried to use Bayes Rule to prove it but it doesn't work. I think it might actually be wrong... but I just cannot think about an example...
Thanks for your help!

Another counter e.g.  take $X$ and $Y$ to be any two independent events, and let $Z$ be the same as $X$.
