Elementary Probability 2nd Edition by David Stirzaker ISBN 0521534283 9780521534284

0. Introduction

• 0.1 Chance

• 0.2 Models

• 0.3 Symmetry

• 0.4 The Long Run

• 0.5 Pay-Offs

• 0.6 Introspection

• 0.7 FAQs

• 0.8 History

• Appendix: Review of Elementary Mathematical Prerequisites

1. Probability

• 1.1 Notation and Experiments

• 1.2 Events

• 1.3 The Addition Rules for Probability

• 1.4 Properties of Probability

• 1.5 Sequences of Events

• 1.6 Remarks

• 1.7 Review and Checklist for Chapter 1

• Worked examples and exercises

  • 1.8 Example: Dice

  • 1.9 Example: Urn

  • 1.10 Example: Cups and Saucers

  • 1.11 Example: Sixes

  • 1.12 Example: Family Planning

  • 1.13 Example: Craps

  • 1.14 Example: Murphy’s Law

• Problems

2. Conditional Probability and Independence

• 2.1 Conditional Probability

• 2.2 Independence

• 2.3 Recurrence and Difference Equations

• 2.4 Remarks

• 2.5 Review and Checklist for Chapter 2

• Worked examples and exercises

  • 2.6 Example: Sudden Death

  • 2.7 Example: Polya’s Urn

  • 2.8 Example: Complacency

  • 2.9 Example: Dogfight

  • 2.10 Example: Smears

  • 2.11 Example: Gambler’s Ruin

  • 2.12 Example: Accidents and Insurance

  • 2.13 Example: Protocols

  • 2.14 Example: Eddington’s Controversy

• Problems

3. Counting

• 3.1 First Principles

• 3.2 Permutations: Ordered Selection

• 3.3 Combinations: Unordered Selection

• 3.4 Inclusion–Exclusion

• 3.5 Recurrence Relations

• 3.6 Generating Functions

• 3.7 Techniques

• 3.8 Review and Checklist for Chapter 3

• Worked examples and exercises

  • 3.9 Example: Railway Trains

  • 3.10 Example: Genoese Lottery

  • 3.11 Example: Ringing Birds

  • 3.12 Example: Lottery

  • 3.13 Example: The Ménages Problem

  • 3.14 Example: Identity

  • 3.15 Example: Runs

  • 3.16 Example: Fish

  • 3.17 Example: Colouring

  • 3.18 Example: Matching (Rencontres)

• Problems

4. Random Variables: Distribution and Expectation

• 4.1 Random Variables

• 4.2 Distributions

• 4.3 Expectation

• 4.4 Conditional Distributions

• 4.5 Sequences of Distributions

• 4.6 Inequalities

• 4.7 Review and Checklist for Chapter 4

• Worked examples and exercises

  • 4.8 Example: Royal Oak Lottery

  • 4.9 Example: Misprints

  • 4.10 Example: Dog Bites: Poisson Distribution

  • 4.11 Example: Guesswork

  • 4.12 Example: Gamblers Ruined Again

  • 4.13 Example: Postmen

  • 4.14 Example: Acme Gadgets

  • 4.15 Example: Roulette and the Martingale

  • 4.16 Example: Searching

  • 4.17 Example: Duelling

  • 4.18 Binomial Distribution: The Long Run

  • 4.19 Example: Uncertainty and Entropy

• Problems

5. Random Vectors: Independence and Dependence

• 5.1 Joint Distributions

• 5.2 Independence

• 5.3 Expectation

• 5.4 Sums and Products of Random Variables: Inequalities

• 5.5 Dependence: Conditional Expectation

• 5.6 Simple Random Walk

• 5.7 Martingales

• 5.8 The Law of Averages

• 5.9 Convergence

• 5.10 Review and Checklist for Chapter 5

• Worked examples and exercises

  • 5.11 Example: Golf

  • 5.12 Example: Joint Lives

  • 5.13 Example: Tournament

  • 5.14 Example: Congregations

  • 5.15 Example: Propagation

  • 5.16 Example: Information and Entropy

  • 5.17 Example: Cooperation

  • 5.18 Example: Strange But True

  • 5.19 Example: Capture–Recapture

  • 5.20 Example: Visits of a Random Walk

  • 5.21 Example: Ordering

  • 5.22 Example: More Martingales

  • 5.23 Example: Simple Random Walk Martingales

  • 5.24 Example: You Can’t Beat the Odds

  • 5.25 Example: Matching Martingales

  • 5.26 Example: Three-Handed Gambler’s Ruin

• Problems

6. Generating Functions and Their Applications

• 6.1 Introduction

• 6.2 Moments and the Probability Generating Function

• 6.3 Sums of Independent Random Variables

• 6.4 Moment Generating Functions

• 6.5 Joint Generating Functions

• 6.6 Sequences

• 6.7 Regeneration

• 6.8 Random Walks

• 6.9 Review and Checklist for Chapter 6

• Appendix: Calculus

• Worked examples and exercises

  • 6.10 Example: Gambler’s Ruin and First Passages

  • 6.11 Example: “Fair” Pairs of Dice

  • 6.12 Example: Branching Process

  • 6.13 Example: Geometric Branching

  • 6.14 Example: Waring’s Theorem: Occupancy Problems

  • 6.15 Example: Bernoulli Patterns and Runs

  • 6.16 Example: Waiting for Unusual Light Bulbs

  • 6.17 Example: Martingales for Branching

  • 6.18 Example: Wald’s Identity

  • 6.19 Example: Total Population in Branching

• Problems

7. Continuous Random Variables

• 7.1 Density and Distribution

• 7.2 Functions of Random Variables

• 7.3 Simulation of Random Variables

• 7.4 Expectation

• 7.5 Moment Generating Functions

• 7.6 Conditional Distributions

• 7.7 Ageing and Survival

• 7.8 Stochastic Ordering

• 7.9 Random Points

• 7.10 Review and Checklist for Chapter 7

• Worked examples and exercises

  • 7.11 Example: Using a Uniform Random Variable

  • 7.12 Example: Normal Distribution

  • 7.13 Example: Bertrand’s Paradox

  • 7.14 Example: Stock Control

  • 7.15 Example: Obtaining Your Visa

  • 7.16 Example: Pirates

  • 7.17 Example: Failure Rates

  • 7.18 Example: Triangles

  • 7.19 Example: Stirling’s Formula

• Problems

8. Jointly Continuous Random Variables

• 8.1 Joint Density and Distribution

• 8.2 Change of Variables

• 8.3 Independence

• 8.4 Sums, Products, and Quotients

• 8.5 Expectation

• 8.6 Conditional Density and Expectation

• 8.7 Transformations: Order Statistics

• 8.8 The Poisson Process: Martingales

• 8.9 Two Limit Theorems

• 8.10 Review and Checklist for Chapter 8

• Worked examples and exercises

  • 8.11 Example: Bivariate Normal Density

  • 8.12 Example: Partitions

  • 8.13 Example: Buffon’s Needle

  • 8.14 Example: Targets

  • 8.15 Example: Gamma Densities

  • 8.16 Example: Simulation – The Rejection Method

  • 8.17 Example: The Inspection Paradox

  • 8.18 Example: von Neumann’s Exponential Variable

  • 8.19 Example: Maximum from Minima

  • 8.20 Example: Binormal and Trinormal

  • 8.21 Example: Central Limit Theorem

  • 8.22 Example: Poisson Martingales

  • 8.23 Example: Uniform on the Unit Cube

  • 8.24 Example: Characteristic Functions

• Problems

9. Markov Chains

• 9.1 The Markov Property

• 9.2 Transition Probabilities

• 9.3 First Passage Times

• 9.4 Stationary Distributions

• 9.5 The Long Run

• 9.6 Markov