\[ \newcommand{\nRV}[2]{{#1}_1, {#1}_2, \ldots, {#1}_{#2}} \newcommand{\pnRV}[3]{{#1}_1^{#3}, {#1}_2^{#3}, \ldots, {#1}_{#2}^{#3}} \newcommand{\onRV}[2]{{#1}_{(1)} \le {#1}_{(2)} \le \ldots \le {#1}_{(#2)}} \newcommand{\RR}{\mathbb{R}} \newcommand{\Prob}[1]{\mathbb{P}\left({#1}\right)} \newcommand{\PP}{\mathcal{P}} \newcommand{\iidd}{\overset{\mathsf{iid}}{\sim}} \newcommand{\X}{\times} \newcommand{\EE}[1]{\mathbb{E}\left[{#1}\right]} \newcommand{\Var}[1]{\mathsf{Var}\left({#1}\right)} \newcommand{\Ber}[1]{\mathsf{Ber}\left({#1}\right)} \newcommand{\Geom}[1]{\mathsf{Geom}\left({#1}\right)} \newcommand{\Bin}[1]{\mathsf{Bin}\left({#1}\right)} \newcommand{\Poi}[1]{\mathsf{Pois}\left({#1}\right)} \newcommand{\Exp}[1]{\mathsf{Exp}\left({#1}\right)} \newcommand{\SD}[1]{\mathsf{SD}\left({#1}\right)} \newcommand{\sgn}[1]{\mathsf{sgn}} \newcommand{\dd}[1]{\operatorname{d}\!{#1}} \]

Chapter 2 Review of Basic probability

“Information: the negative reciprocal value of probability.”

— Claude Elwood Shannon

This chapter provides an overview of basic probability concepts. It begins with an introduction to the most common distributions, followed by a discussion of the Markov inequality, Chebyshev inequality, and the Central Limit Theorem. These tools are essential for understanding probability theory. Additionally, the chapter covers descriptive statistics for summarising data.

It also includes important distributions such as the chi-squared, t, and F distributions. They are crucial in statistical tests and decision-making.