This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons…

This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also…

The target audience for this book is college students who are required to learn statistics, students with little background in mathematics and often no motivation to learn more. It is assumed that the students do have basic skills in using computers…

This text is for an introductory level probability and statistics course with an intermediate algebra prerequisite. The focus of the text follows the American Statistical Association’s Guidelines for Assessment and Instruction in Statistics Education…

The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in…

The subject of this chapter is fuzzy sets and the basic issues related to them. The first section discusses concepts of sets: classic and fuzzy, and presents various ways of describing fuzzy sets. The second section is dedicated to t-norms, s-norms,…

The application of wearable electronics in the biomedical research and commercial fields has
been gaining great interest over the last several decades. Small-sized, lightweight monitoring systems
with low-power consumption and, of course,…

Throughout industry and science it is common today to study nature or technological devices through models on a computer. With such models the computer acts as a virtual lab where experiments can be done in a fast, reliable, safe, and cheap way. In…

Optimal scheduling is an important area of operations research, as it has both theoretical and
practical aspects. It is clear that efficient algorithms are most desirable for practical applications,
since most real-world scheduling problems have…

This text is intended to support courses that bridge the divide between mathematics typically encountered in U.S. high school curricula and the practical problems that natural resource students might engage with in their disciplinary coursework and…

Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge.…

We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through…

The concepts and basic topics in elementary Linear Algebra and Calculus are reviewed and generalized to Linear Analysis in this first unit. In particular, the dot product, the vector space of R 2(that is, the x − y plane in Plane Geometry), and…

Mathematical definitions should be perfectly precise because they do not describe something which is observed out there in the world, since such descriptive definitions might have fuzzy edges. In biology, for example, whether a virus is considered…

You are exposed to statistics regularly. If you are a sports fan, then you have the statistics for your favorite player. If you are interested in politics, then you look at the polls to see how people feel about certain issues or candidates. If you…

This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a…

This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are…

This course is about a large and complex set of statistical methods tied together by a unifying conceptual framework known as “The General Linear Model” (GLM). This model can be used to answer an amazing variety of research questions within an…

ntroductory Statistics is designed for the one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it…

The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. The inaugural effort is OpenIntro Statistics. Probability is…

This book starts by presenting an overview of the statistical thought process. By the end of chapter 2, students are already familiar with concepts such as hypotheses, level of significance, p-values, errors. Normally these topics are not introduced…