A Level Further Statistics 1, Chapter 7 · exam-style questions with mark schemes · probability generating functions $\mathrm{G}_X(t) = \mathrm{E}(t^X)$, the generating functions of the binomial, Poisson, geometric, negative binomial and discrete uniform distributions, probabilities from coefficients and derivatives, $\mathrm{E}(X)$ and $\mathrm{Var}(X)$ from $\mathrm{G}_X'(1)$ and $\mathrm{G}_X''(1)$, unknown constants from $\mathrm{G}_X(1) = 1$, and the generating functions of $aX + b$ and of sums of independent random variables