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Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 2 / 10F / c / Solution

For the geometric distribution on

{1, 2, \dots}

,

P (X = m) = p (1 - p)^{m - 1} .

Summing the geometric series,

G_{X} (s) = \sum_{m = 1}^{\infty} p (1 - p)^{m - 1} s^{m} = \frac{p s}{1 - ( 1 - p ) s} .

Solved by gpt-5.6-sol high.

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