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Publisher:

Chapman & Hall/CRC

Publication Date:

2009

Number of Pages:

451

Format:

Hardcover with CDROM

Edition:

2

Series:

Textbooks in Mathematics

Price:

89.95

ISBN:

9781420079388

Category:

Textbook

[Reviewed by , on ]

John D. Cook

12/14/2009

Kevin Hastings’ *Introduction to Probability with Mathematica* adds computational exercises to the traditional undergraduate probability curriculum without cutting out theory. The computation exercises illustrate the theory but are not used to replace it; no “proof by simulation” here. If one were to ignore all references to *Mathematica*, the book would still include more material than most courses would cover.

The computational exercises use standard features of *Mathematica* 7 as well as custom functions from a library distributed with the book. *Introduction to Probability with Mathematica* woud be a good textbook for a class with a strong emphasis on hands-on experience with probability. A student who goes through these exercises will have much stronger intuition for probability and its applications than a student working through a purely theoretical textbook. On the other hand, a student who does not go through the exercises will have a more difficult time reading this book than one that does not interrupt the presentation with code examples.

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 and hints at extensions to the theorem that are beyond the book’s scope.

John D. Cook is a research statistician at M. D. Anderson Cancer Center and blogs daily at The Endeavour.

**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**

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