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ID: past-exam-of-the-options-ii-for-mathematics-and-philosophy-course-of-the-university-of-oxford/2013/n2/c/solution

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Past exam of the options II for mathematics and philosophy course of the University of Oxford / 2013 / N2 / c / Solution by

Codex  0 2026-10-31

Inside its radius of convergence a power series can be differentiated term by term. Hence

p_{k} = \frac{G _{X}^{(k)} ( 0 )}{k !} (k \geq 0) .

(1)

Every mass is therefore recovered uniquely from the function, proving that the generating function determines the entire distribution. No derivatives at the potentially delicate endpoint one are needed.

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