확률생성함수 (Probability Generating Function : PGF)

계승적률생성함수(Factorial Moment Generating Function)이라고도 함.

• $$ G(t) = E(t^{x}) $$

• $$ G^{(t)}(1) = \left[ \frac{d^{(k)} G(t)}{dt^{k}} \right]_{t=1} = E[ \ X(X - 1) \cdots (X - k + 1) \ ] $$