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10 cards from this deck
GX(t)=โx=0โpxtxG_X(t) = \sum_{x=0}^\infty p_x t^xGXโ(t)=โx=0โโpxโtx
A dummy variable (not a probability)
111
1x!dxdtxGX(t)โฃt=0\frac{1}{x!} \frac{d^x}{dt^x} G_X(t) \bigg|_{t=0}x!1โdtxdxโGXโ(t)โt=0โ
GX(t)=[pt+(1โp)]nG_X(t) = [pt + (1-p)]^nGXโ(t)=[pt+(1โp)]n
GX(t)=eฮป(tโ1)G_X(t) = e^{\lambda(t-1)}GXโ(t)=eฮป(tโ1)
GX(t)=p1โ(1โp)tG_X(t) = \frac{p}{1-(1-p)t}GXโ(t)=1โ(1โp)tpโ
GX(t)=(p1โ(1โp)t)rG_X(t) = \left(\frac{p}{1-(1-p)t}\right)^rGXโ(t)=(1โ(1โp)tpโ)r
Mean and variance
Differentiate and evaluate at t=0t=0t=0
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