Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the external world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-?rst century, as dif?cult new problems emerge, that will require more sophisticated models and analysis. Thisisa text onthe fundamentalsof thetheoryofprobabilityat anundergraduate or ?rst-year graduate level for students in science, engineering,and economics. The only mathematical background required is knowledge of univariate and multiva- ate calculus and basic linear algebra. The book covers all of the standard topics in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random variables. But it also has some unique features and a forwa- looking feel.

Introducing Probability.- The Birthday and Matching Problems.- Conditional Probability and Independence.- Integer-Valued and Discrete Random Variables.- Generating Functions.- Standard Discrete Distributions.- Continuous Random Variables.- Some Special Continuous Distributions.- Normal Distribution.- Normal Approximations and the Central Limit Theorem.- Multivariate Discrete Distributions.- Multidimensional Densities.- Convolutions and Transformations.- Markov Chains and Applications.- Urn Models in Physics and Genetics.