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10 cards from this deck
GX(t)=∑x=0∞pxtxG_X(t) = \sum_{x=0}^\infty p_x t^xGX(t)=∑x=0∞pxtx
A dummy variable (not a probability)
111
1x!dxdtxGX(t)∣t=0\frac{1}{x!} \frac{d^x}{dt^x} G_X(t) \bigg|_{t=0}x!1dtxdxGX(t)t=0
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
Mean and variance
Differentiate and evaluate at t=0t=0t=0
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