Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Discrete mathematics, continuous mathematics and probability / 7 / a / iii

Table of contents
- Solution iii

Solution

The expected value is the derivative of the probability generating function at one. The expression from part (ii) gives

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

Its finiteness also follows directly from the exponentially decaying geometric probabilities.

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