**Discrete Probability**

The Cast of Characters

Properties of Probability

Simulation

Random Sampling

Conditional Probability

Independence

**Discrete Distributions**

Discrete Random Variables, Distributions, and Expectations

Bernoulli and Binomial Random Variables

Geometric and Negative Binomial Random Variables

Poisson Distribution

Joint, Marginal, and Conditional Distributions

More on Expectation

**Continuous Probability**

From the Finite to the (Very) Infinite

Continuous Random Variables and Distributions

Continuous Expectation

**Continuous Distributions**

The Normal Distribution

Bivariate Normal Distribution

New Random Variables from Old

Order Statistics

Gamma Distributions

Chi-Square, Student’s *t*, and *F*-Distributions

Transformations of Normal Random Variables

**Asymptotic Theory**

Strong and Weak Laws of Large Numbers

Central Limit Theorem

**Stochastic Processes and Applications**

Markov Chains

Poisson Processes

Queues

Brownian Motion

Financial Mathematics

**Appendix**

Introduction to *Mathematica *

Glossary of *Mathematica *Commands for Probability

Short Answers to Selected Exercises

**References**

**Index**