Book:A.M. Arthurs/Probability Theory
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A.M. Arthurs: Probability Theory
Published $\text {1965}$, Routledge & Kegan Paul
Subject Matter
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
Source work progress
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