## Overview

This text is intended primarily for readers interested in mathematical probability as applied to mathematics, statistics, operations research, engineering, and computer science. It is also appropriate for mathematically oriented readers in the physical and social sciences. Prerequisite material consists of basic set theory and a firm foundation in elementary calculus, including infinite series, partial differentiation, and multiple integration. Some exposure to rudimentary linear algebra (e.g., matrices and determinants) is also desirable. This text includes pedagogical techniques not often found in books at this level, in order to make the learning process smooth, efficient, and enjoyable.

**KEY TOPICS:** **Fundamentals of Probability: **Probability Basics. Mathematical Probability. Combinatorial Probability. Conditional Probability and Independence. **Discrete Random Variables: **Discrete Random Variables and Their Distributions. Jointly Discrete Random Variables. Expected Value of Discrete Random Variables. **Continuous ****Random Variables: **Continuous Random Variables and Their Distributions. Jointly Continuous Random Variables. Expected Value of Continuous Random Variables. **Limit Theorems and Advanced Topics: **Generating Functions and Limit Theorems. Additional Topics.

**MARKET:**For all readers interested in probability.

## Table of contents

*Chapter Opener and Review appear in each chapter*).

**I. FUNDAMENTALS OF PROBABILITY.**

**1. Probability Basics.**

*Biography: Girolamo Cardano.*

**2. Mathematical Probability.**

*Biography: Andrei Kolmogorov.*

**3. Combinatorial Probability.**

*Biography: James Bernoulli.*

**4. Conditional Probability and Independence.**

*Biography: Thomas Bayes.*

**II. DISCRETE RANDOM VARIABLES.**

**5. Discrete Random Variables and Their Distributions.**

*Biography: Siméon-Dennis Poisson.*

**6. Jointly Discrete Random Variables.**

*Biography: Blaise Pascal.*

**7. Expected Value of Discrete Random Variables.**

*Biography: Christiaan Huygens.*

**III. CONTINUOUS RANDOM VARIABLES.**

**8. Continuous Random Variables and Their Distributions.**

*Biography: Carl Friedrich Gauss.*

**9. Jointly Continuous Random Variables.**

*Biography: Pierre de Fermat.*

**10. Expected Value of Continuous Random Variables.**

*Biography: Pafnuty Chebyshev.*

**IV. LIMIT THEOREMS AND ADVANCED TOPICS.**

**11. Generating Functions and Limit Theorems.**

*Biography: William Feller.*

**12. Additional Topics.**

*Biography: Sir Ronald Fisher.*

**Appendices.**

**Index.**

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