 Solution

ID: 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/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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