Book:Geoffrey Grimmett/Probability: An Introduction
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Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction
Published $\text {1986}$, Oxford Science Publications
- ISBN 0-19-853264-4
Subject Matter
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
Further Editions
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
- 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $1$: Events and probabilities: $1.4$: Probability spaces: Exercise $7$