\[ \newcommand{\Exg}{\operatorname{\mathbb{E}}} \newcommand{\Ex}{\mathbb{E}} \newcommand{\Ind}{\mathbb{I}} \newcommand{\Var}{\operatorname{Var}} \newcommand{\Cov}{\operatorname{Cov}} \newcommand{\Corr}{\operatorname{Corr}} \newcommand{\ee}{\mathrm{e}} \]

11  LCGs

Summary:

• Linear congruential generators are pseudorandom number generators based on the recurrence \(x_{n+1} = (ax_n + c) \bmod m\).

• Any LCG will eventually repeat with periodic behaviour.

• Suppose \(m\) is a power of 2. Then an LCG has period \(m\) if and only if \(c\) is odd and \(a = 1 \bmod 4\).

You should now be able to answer all questions on Problem Sheet 2. Your answer will be discussed in the problems class on Thursday 31 October.

Read more: Voss, An Introduction to Statistical Computing, Subsections 1.1.1 and 1.1.2.