Book:Geoffrey Grimmett/Probability: An Introduction

Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction

Published $\text {1986}$, Oxford Science Publications

ISBN 0-19-853264-4

Subject Matter

• Probability Theory

Contents

Preface

A. BASIC PROBABILITY

1 Events and probabilities

1.1 Experiments with chance

1.2 Outcomes and events

1.3 Probabilities

1.4 Probability spaces

1.5 Discrete sample spaces

1.6 Conditional probabilities

1.7 Independent events

1.8 The partition theorem

1.9 Probability measures are continuous

1.10 Worked problems

1.11 Problems

2 Discrete random variables

2.1 Probability mass functions

2.2 Examples

2.3 Functions of discrete random variables

2.4 Expectation

2.5 Conditional expectation and the partition theorem

2.6 Problems

3 Multivariate discrete distributions and independence

3.1 Bivariate discrete distributions

3.2 Expectation in the multivariate case

3.3 Independence of discrete random variables

3.4 Sums of random variables

4 Probability generating functions

4.1 Generating functions

4.2 Integer-valued random variables

4.3 Moments

4.4 Sums of independent random variables

4.5 Problems

5 Distribution functions and density functions

5.1 Distribution functions

5.2 Examples of distribution functions

5.3 Continuous random variables

5.4 Some common density functions

5.5 Functions of random variables

5.6 Expectations of continuous random variables

5.7 Problems

B. FURTHER PROBABILITY

6 Multivariate distributions and independence

6.1 Random vectors and independence

6.2 Joint density functions

6.3 Marginal density functions and independence

6.4 Sums of continuous random variables

6.5 Changes of variables

6.6 Conditional density functions

6.7 Expectations of continuous random variables

6.8 Conditional expectation and the bivariate normal distribution

6.9 Problems

7 Moments, and moment generating functions

7.1 A general note

7.2 Moments

7.3 Variance and covariance

7.4 Moment generating functions

7.5 Characteristic functions

7.6 Problems

8 The two main limit theorems

8.1 The law of averages

8.2 Chebyshev's inequality and the weak law

8.3 The central limit theorem

8.4 Convergence in distribution, and characteristic functions

8.5 Problems

C. RANDOM PROCESSES

9 Branching processes

9.1 Random processes

9.2 A model for population growth

9.3 The generating-function method

9.4 An example

9.5 The probability of extinction

9.6 Problems

10 Random walks

10.1 One-dimensional random walks

10.2 Transition probabilities

10.3 Recurrence and transience in random walks

10.4 The Gambler's Ruin problem

10.5 Problems

11 Random processes in continuous time

11.1 Life at a telephone exchange

11.2 Poisson processes

11.3 Inter-arrival times and the exponential distribution

11.4 Population growth and the simple birth process

11.5 Birth and death processes

11.6 A simple queueing model

11.7 Problems

Appendix: Difference equations

Answers to exercises

Remarks on the problems

Reading list

Index

Next

Further Editions

• 2014: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction (2nd ed.)

Source work progress

• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 5.1$: Distribution Functions

Redoing from start: examples and exercises to be covered

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