Course in Probability

This text is intended primarily for a first course in mathematical probability for students in mathematics, statistics, operations research, engineering, and computer science. It is also appropriate for mathematically oriented students in the physical and social sciences. Prerequisite material consists of basic set theory and a firm foundation in elementary calculus, including infinite series, partial differentiation, and multiple integration. Some exposure to rudimentary linear algebra (e.g., matrices and determinants) is also desirable. This text includes pedagogical techniques not often found in books at this level, in order to make the learning process smooth, efficient, and enjoyable.Illustrative examples. Definition and results (e.g., theorems and propositions) are followed by one or more examples that illustrate the concept or result in order to provide a concrete frame of reference. Abundant & varied exercises. The text contains an abundance of exercises, far more than most other probability books. The exercises provide an opportunity to vary the coverage and level. Applications. A diverse collection of applications appear throughout the text, some as examples or exercises, and others as entire sections. The last chapter of the text, Chapter 12, provides introductory materials-independent of one another-for three main follow-up courses: mathematical statistics, stochastic processes, and operations research. Biographies. Each chapter begins with a brief biography of a famous probabilist, mathematician, statistician, or scientist who has made substantial contributions to probability theory or its applications. These biographies help students obtain a perspective on how probability and its applications have developed. Motivation of key concepts. The importance of and rationale behind ideas such as the axioms of probability, conditional probability, independence, random variables, joint and conditional distributions, and expected value are made transparent. Formulas for probability mass functions and probability density functions are motivated instead of only stated. This helps students understand how such formulas arise naturally.