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

10  Generating random numbers

Summary:

• Random number generation has two problems: how to generate uniform random numbers between 0 and 1, and how to convert these to your desired distribution.

• Uniform random numbers can be generated from true physical randomness (which will definitely be totally random, but will be slow and expensive) or using a pseudorandom number generator on a computer (which is very fast, but needs to be designed carefully to ensure a random-looking output).

• LCGs are a type of pseudorandom number generator that are started from a “seed”, which can be chosen using physical randomness or set by the user.

Read more: Voss, An Introduction to Statistical Computing, introduction to Chapter 1, introduction to Section 1.1, and Subsection 1.1.3.