Book:A.M. Arthurs/Probability Theory

A.M. Arthurs: Probability Theory

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

Subject Matter

• Probability Theory

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

Answers to Exercises

Suggestions for Further Reading

Index

Next

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