A counting variable is a discrete random variable that ranges in the natural number. For each counting variable $X,$ define its generating function $f_X$ to be the polynomial $\sum_{i=0}^\infty P(X=k)t^k.$ If two random variables are independent then we know $f_{X+Y}=f_Xf_Y.$ Yet I want to find an example that $X,Y$ are not even uncorrelated but $f_{X+Y}=f_Xf_Y.$
2026-04-04 05:23:55.1775280235
Generating function does not imply uncorrelation.
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