Introduction to Probability Models Audiobook

According to Leo Breiman (1968), probability theory has a right and a left hand. The right hand refers to rigorous mathematics, and the left hand refers to 'proba­ bilistic thinking'. The combination of these two aspects makes probability theory one of the most exciting fields in mathematics. One can study probability as a purely mathematical enterprise, but even when you do that, all the concepts that arise do have a meaning on the intuitive level. For instance, we have to define what we mean exactly by independent events as a mathematical concept, but clearly, we all know that when we flip a coin twice, the event that the first gives heads is independent of the event that the second gives tails. Why have I written this book? I have been teaching probability for more than fifteen years now, and decided to do something with this experience. There are already many introductory texts about probability, and there had better be a good reason to write a new one. I will try to explain my reasons now.

This book introduces and studies a number of stochastic models of subsistence, communication, social evolution and political transition that will allow the reader to grasp the role of uncertainty as a fundamental property of our irreversible world. At the same time, it aims to bring about a more interdisciplinary and quantitative approach across very diverse fields of research in the humanities and social sciences.

The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete and continuous states. Applications include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds of genetic modeling.

Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study.