I've come across a statistics problem that I can't seem to figure out how to solve:
"A certain discrete random variable has probability generating function: $ \pi_x(q) = \dfrac{1}{3}\dfrac{2+q}{2-q} $ Compute p(x) for x = 0,1,2,3,4,5. (Hint: the formula for summing a geometric series will help you expand the denominator)."
I'm not entirely sure what sort of answer this problem requires. q is not given, so is it only possible to solve this in terms of q? What would be a good way to start solving this problem (especially since I don't know of any way to solve for p(x) given a probability generating function)? Any help would be greatly appreciated.