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|