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GX(t)=∑x=0∞P(X=x)txG_X(t) = \sum_{x=0}^\infty P(X = x) t^xGX(t)=∑x=0∞P(X=x)tx
GX(t)=[pt+(1−p)]nG_X(t) = [pt + (1-p)]^nGX(t)=[pt+(1−p)]n
GX(t)=eλ(t−1)G_X(t) = e^{\lambda(t-1)}GX(t)=eλ(t−1)
GX(t)=p1−(1−p)tG_X(t) = \frac{p}{1 - (1-p)t}GX(t)=1−(1−p)tp
GX(t)=(p1−(1−p)t)rG_X(t) = \left(\frac{p}{1 - (1-p)t}\right)^rGX(t)=(1−(1−p)tp)r
E[X]=GX′(1)\mathbb{E}[X] = G_X'(1)E[X]=GX′(1)
Var(X)=GX′′(1)+GX′(1)−[GX′(1)]2\text{Var}(X) = G_X''(1) + G_X'(1) - [G_X'(1)]^2Var(X)=GX′′(1)+GX′(1)−[GX′(1)]2
E[X]=np\mathbb{E}[X] = npE[X]=np
Var(X)=λ\text{Var}(X) = \lambdaVar(X)=λ
∣t∣<11−p|t| < \frac{1}{1-p}∣t∣<1−p1
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