Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Discrete mathematics, probability and continuous mathematics / 7 / a / i

For a discrete random variable taking nonnegative integer values, its probability generating function isIt is defined at least for $|s|\le 1$. The usual probability generating function is intended for nonnegative integer-valued random variables; a general discrete real-valued random variable need not have this form. The coefficient of $s^k$ recovers $\mathbb{P}(X=k)$.