Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability (resit) / 8 / a / ii / Solution

Let $S_n={\sum }_{i=1}^n{X}_i$. By independence, the expectation of a product of independent random variables factors, and the identical distributions giveThis is valid for $|s|\le 1$ and wherever the required absolute expectations exist. It is the probability generating function of an independent sum.