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GZ(t)=GX(t)รGY(t)G_Z(t) = G_X(t) \times G_Y(t)GZโ(t)=GXโ(t)รGYโ(t)
GZ(t)=GX(ta)G_Z(t) = G_X(t^a)GZโ(t)=GXโ(ta)
GZ(t)=tcGX(t)G_Z(t) = t^c G_X(t)GZโ(t)=tcGXโ(t)
E[Z]=E[X]+E[Y]\mathbb{E}[Z] = \mathbb{E}[X] + \mathbb{E}[Y]E[Z]=E[X]+E[Y]
Var(Z)=Var(X)+Var(Y)\text{Var}(Z) = \text{Var}(X) + \text{Var}(Y)Var(Z)=Var(X)+Var(Y)
GX(t)=eฮป(tโ1)G_X(t) = e^{\lambda(t-1)}GXโ(t)=eฮป(tโ1)
GX(t)=[pt+(1โp)]nG_X(t) = [pt + (1-p)]^nGXโ(t)=[pt+(1โp)]n
GX(t)=p1โ(1โp)tG_X(t) = \frac{p}{1-(1-p)t}GXโ(t)=1โ(1โp)tpโ
When XXX and YYY are independent
Po(ฮป1+ฮป2)\text{Po}(\lambda_1 + \lambda_2)Po(ฮป1โ+ฮป2โ)
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