I know you need to integrate f(x,y) with respect to y (gives f(y)) and f(x,y) with respect to x (gives f(x))between oo and oo+ and verify the equation f(x,y) = f(x)f(y), but I don't know what to do when we have joint probability mass functions.

I know you need to integrate f(x,y) with respect to y (gives f(y)) and f(x,y) with respect to x (gives f(x))between oo and oo+ and verify the equation f(x,y) = f(x)f(y), but I don't know what to do when we have joint probability mass functions.
In this context what do you mean by "joint probability mass function"? Isn't it simply f(x,y)?
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