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

X,Y,Z are random variables. How to construct an example when X and Z are correlated, Y and Z are correlated, but X and Y are independent?

Answer

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

Attribution
Source : Link , Question Author : Charlotte , Answer Author : fblundun

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