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2829概率中等derivationmedium

A Geometric Number of Bernoulli Trials

题目

Let NN have the geometric law on {0,1,2,}\{0,1,2,\dots\} with P(N=n)=p(1p)nP(N=n)=p(1-p)^n. Conditional on NN, let \[ S=\sum_{i=1}^N X_i, \] where the XiX_i are i.i.d. Bernoulli(q)(q). Find the PGF of SS and identify its distribution.

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你的答案

PGF of S

Success parameter of S