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확률생성함수 (Probability Generating Function : PGF)

정의

계승적률생성함수(Factorial Moment Generating Function)이라고도 함.

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