# Example where XX and ZZ are correlated, YY and ZZ are correlated, but XX and YY are independent

$$X,Y,ZX,Y,Z$$ are random variables. How to construct an example when $$XX$$ and $$ZZ$$ are correlated, $$YY$$ and $$ZZ$$ are correlated, but $$XX$$ and $$YY$$ are independent?

Intuitive example: $$Z=X+YZ = X + Y$$, where $$XX$$ and $$YY$$ are any two independent random variables with finite nonzero variance.