Introduction to Probability with Mathematica, Second Edition

Introduction to Probability with Mathematica, Second Edition

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Features

  • 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 7.0

Solutions manual available for qualifying instructors

Summary

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 Mathematica. It provides a real understanding of probabilistic modeling and the analysis of data and encourages the application of these ideas to practical problems. The accompanying CD-ROM offers instructors the option of creating class notes, demonstrations, and projects.

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.

Table of Contents

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

Author Bio(s)

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

Editorial Reviews

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