- Uses simulation to help students understand randomness and sampling concepts better
- Covers the graphical technique of the normal quantile plot
- Harnesses the interactive aspects of
*Mathematica*to highlight the visual appeal of examples and produce interesting animations - Includes a CD-ROM that contains a
*Mathematica*notebook for each section in the book, along with the KnoxProb6`Utilities`and KnoxProb7`Utilities` packages for users of*Mathematica*6.0 and

*Solutions manual available for qualifying instructors*

Updated to conform to *Mathematica*^{®} 7.0, **Introduction** **to Probability with Mathematica^{®}, Second Edition** continues to show students how to easily create simulations from templates and solve problems using

**New to the Second Edition**

- Expanded section on Markov chains that includes a study of absorbing chains
- New sections on order statistics, transformations of multivariate normal random variables, and Brownian motion
- More example data of the normal distribution
- More attention on conditional expectation, which has become significant in financial mathematics
- Additional problems from Actuarial Exam P
- New appendix that gives a basic introduction to
*Mathematica* - New examples, exercises, and data sets, particularly on the bivariate normal distribution
- New visualization and animation features from
*Mathematica*7.0 - Updated
*Mathematica*notebooks on the CD-ROM

After covering topics in discrete probability, the text presents a fairly standard treatment of common discrete distributions. It then transitions to continuous probability and continuous distributions, including normal, bivariate normal, gamma, and chi-square distributions. The author goes on to examine the history of probability, the laws of large numbers, and the central limit theorem. The final chapter explores stochastic processes and applications, ideal for students in operations research and finance.

**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**

**Kevin J. Hastings** is a professor of mathematics at Knox College in Galesburg, Illinois.

If you own the first edition, you will be very pleased with the second edition. It is more complete, better organized, and even more well-presented. If you don’t own the first edition, and are looking for an effective tool for conveying probabilistic concepts, Hastings’ book should certainly be one you consider.

—Jane L. Harvill, *The American Statistician*, November 2011

**Introduction to Probability with Mathematica** adds computational exercises to the traditional undergraduate probability curriculum without cutting out theory. … a good textbook for a class with a strong emphasis on hands-on experience with probability. … One interesting feature of the book is that each set of exercises includes a few problems taken from actuarial exams. No doubt this will comfort students who are taking a probability course in hopes that it will prepare them for an actuarial exam. Another interesting feature is the discussion of the Central Limit Theorem. The book goes into an interesting discussion of the history of the theorem … .

—*MAA Reviews,* December 2009