Hastings Introduction to Probability with Mathematica, Second Edition

2. Auflage 2011
ISBN: 978-1-4200-7940-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 465 Seiten

Reihe: Textbooks in Mathematics

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.

Zielgruppe

Undergraduate students of mathematics, statistics, and actuarial science.

Autoren/Hrsg.

Hastings, Kevin J.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Bayesianische Inferenz

Inhaltsverzeichnis

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

Über Autor(innen)

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