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Topic: Sampling and probability generating functions - reference wanted
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Stephen Montgomery-Smith

Posts: 86
Registered: 11/24/07
Sampling and probability generating functions - reference wanted
Posted: Oct 7, 2012 10:21 PM
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Suppose I have a huge (effectively infinite) population of widgets. The number of widgets that are broken is given by a random variable X, whose probability generating function is p(z) = E(z^X).

Now suppose I look at a proportion theta (0<=theta<=1) of the population. Let Y be the random variable of the number of broken widgets in this proportion. Then it is easily shown that the probability generating function for Y is p(1-theta(1-z)).

What is a book that contains this fact so that I can reference it?

Thanks, Stephen

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