Probability Models Springer Undergraduate Mathematics Series 2nd edition by John Haigh ISBN 1447153421 978-1447153429

I don’t have direct access to the specific table of contents for Probability Models (2nd edition) from the Springer Undergraduate Mathematics Series, but based on the general content and structure of probability textbooks at the undergraduate level, I can offer a plausible outline of what the table of contents might look like. Here’s a possible structure based on typical topics in probability theory:

Table of Contents

Preface

Chapter 1: Introduction to Probability

• The Concept of Probability
• Sample Spaces and Events
• Axioms of Probability
• Basic Counting Principles
• Conditional Probability and Independence

Chapter 2: Random Variables and Distributions

• Random Variables and Their Types
• Discrete Random Variables and Probability Mass Functions (PMF)
• Continuous Random Variables and Probability Density Functions (PDF)
• Cumulative Distribution Functions (CDF)
• Expected Value, Variance, and Moments

Chapter 3: Special Probability Distributions

• Discrete Distributions: Binomial, Poisson, and Geometric Distributions
• Continuous Distributions: Uniform, Normal, Exponential, and Gamma Distributions
• Moment-Generating Functions
• The Central Limit Theorem

Chapter 4: Joint Probability Distributions

• Joint Distribution of Two or More Random Variables
• Marginal and Conditional Distributions
• Covariance and Correlation
• Independence of Random Variables
• Transformations of Random Variables

Chapter 5: Functions of Random Variables

• Distribution of Functions of One Random Variable
• Distribution of Sums and Products of Random Variables
• Methods of Transformation (e.g., Jacobian method)
• The Law of Large Numbers

Chapter 6: Markov Chains

• Discrete-Time Markov Chains
• Transition Matrices and States
• Long-Term Behavior and Stationary Distributions
• First-Passage Times and Recurrence
• Applications of Markov Chains

Chapter 7: Limit Theorems

• Weak Law of Large Numbers
• Strong Law of Large Numbers
• Central Limit Theorem (CLT) and its Applications
• Poisson Approximation

Chapter 8: Bayesian Inference

• Bayes’ Theorem and Its Applications
• Posterior Distribution and Prior Information
• Maximum Likelihood Estimation
• Bayesian vs. Frequentist Methods

Chapter 9: Simulation and Monte Carlo Methods

• Random Number Generation
• Monte Carlo Simulation
• Applications of Simulation in Probability Models
• Importance Sampling

Chapter 10: Queuing Theory and Applications

• Basic Queuing Models (M/M/1, M/G/1)
• Little’s Law
• Performance Measures in Queuing Systems
• Applications to Computer Networks and Service Systems

Chapter 11: Introduction to Stochastic Processes

• Definition of Stochastic Processes
• Poisson Process and Applications
• Birth-Death Processes
• Applications in Finance and Biology

Chapter 12: Advanced Topics (Optional)

• Renewal Theory
• Continuous-Time Markov Chains
• Advanced Limit Theorems

Appendices

• Mathematical Tools (Integrals, Series, etc.)
• Tables of Distributions
• Solutions to Selected Problems

Index