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For $X_i \\overset{\\text{iid}}{\\sim} X$

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And $N$ as a discrete random variable with PGF given by $P_N(s)$

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Let $Y = X_1 + X_2 + \\cdots + X_N$

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What is the formula for the PGF of Y: $P_Y(s)$?

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$P_Y(s)=P_N(P_X(s))$

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