Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics III / 4 / a / iii

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- Solution iii

Solution

The mean is the derivative at one of the probability generating function. Therefore

E X = G_{X}^{'} (1) = \frac{p}{p ^{2}} = \frac{1}{p} .

Evaluation at one is valid here because the probability generating function has radius of convergence

1/ (1 - p) > 1

.

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