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

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- Solution i

Solution

For a nonnegative integer-valued random variable, its probability generating function is

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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