Book:A.M. Arthurs/Probability Theory

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