 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability/probability/8/a/i/solution

G_{X} (s) = E [s^{X}] = k = 0 \sum \infty P (X = k) s^{k} .

The series converges absolutely at least for

∣ s ∣ \leq 1

, with

0^{0} = 1

in the

k = 0

term; it may converge on a larger domain.

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