Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well. Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Although the R programs are small in length, they are just as sophisticated and powerful as longer programs in other languages. This brevity makes it easy for readers to become proficient in R.

This calculus-based introduction organizes the material around key themes. One of the most important themes centers on viewing probability as a way to look at the world, helping readers think and reason probabilistically. The text also shows how to combine and link stochastic processes to form more complex processes that are better models of natural phenomena. In addition, it presents a unified treatment of transforms, such as Laplace, Fourier, and z; the foundations of fundamental stochastic processes using entropy and information; and an introduction to Markov chains from various viewpoints. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers.

*...a broad
spectrum of probability and statistics topics ranging from set theory to
statistics and the normal distribution to Poisson process to Markov chains. The
author has covered each topic with an ample depth and with an appreciation of
the problems faced by the modern world. The book contains a rich collection of
exercises and problems ... an excellent introduction to the open source software
R is given in the book... This book showcases interesting, classic puzzles
throughout the text, and readers can also get a glimpse of the lives and
achievements of important pioneers in mathematics...*

From the Foreword, Tianhua Niu, Brigham and Women's Hospital, Harvard Medical School, and Harvard School of Public Health, Boston, Massachusetts, USA |

Features

- Uses R programs and animations throughout to convey important aspects of probability and to encourage experimentation.
- Covers the theorems of probability along with stochastic processes and the relationships among them.
- Deals with probabilistic reasoning in chapters on statistics and conditional probability.
- Introduces transforms via randomization, a unique approach to a very important subject.
- Explores entropy and information to demonstrate basic stochastic processes and the most commonly occurring distributions.
- Shows how Markov chains are a versatile tool for modeling natural phenomena.
- Includes many exercises and selected answers.
- Qualified instructors can obtain PowerPoint slides and
an Instructor's Solutions Manual containing additional exercises and the answers
to all of the exercises. To obtain the slides and manual send a request
to Bob Stern
(
`Bob.Stern@taylorandfrancis.com`). - Errata
- Acknowledgements
- Reviews

Kenneth Paul Baclawski

College of Computer and Information Science

Northeastern University

360 Huntington Avenue

Boston, MA 02115