# Book:A.M. Arthurs/Probability Theory

## A.M. Arthurs: Probability Theory

Published $\text {1965}$, Routledge & Kegan Paul

### Contents

Preface

$1$. Set Theory
$1.1$ Introduction
$1.2$ Sets and subsets
$1.3$ Set operations
Exercise

$2$. Probability and Discrete Sample Spaces
$2.1$ Introduction
$2.2$ Sample spaces and events
$2.3$ Probabilities in discrete sample spaces
$2.4$ Equally likely outcomes
$2.5$ Conditional probability
$2.6$ Independent events
Exercises

$3$. Sample Spaces with Many Elements
$3.1$ Introduction
$3.2$ Permutations and combinations
$3.3$ Subsets and binomial coefficients
$3.4$ Permutations involving identical objects
Exercises

$4$. The Binomial and Poisson Distributions
$4.1$ Bernoulli trials
$4.2$ The binomial distribution
$4.3$ The central term
$4.4$ The law of large numbers
$4.5$ The Poisson approximation
$4.6$ The Poisson distribution
$4.7$ Generating functions
Exercises

$5$. Probability and Continuous Sample Spaces
$5.1$ Introduction
$5.2$ Continuous probability distributions
$5.3$ Probability density functions
$5.4$ The uniform distribution
$5.5$ The normal distribution
$5.6$ The normal approximation to the binomial distribution
Exercises

$6$. Markov Chains
$6.1$ Introduction
$6.2$ Stochastic matrices
$6.3$ $r$ step processes
$6.4$ Ergodic Markov chains
$6.5$ Random walk in one direction
Exercises