I. General theory. Introduction
Basic probability laws
Counting I: cards
Conditional probability, independence, and Bayes' theorem
Counting II: inclusion-exclusion
Counting III: advanced combinatorics
II. Introduction to random variables. Introduction to discrete random variables
Introduction to continuous random variables
Tools: expectation
Tools: Convolutions and changing variables
Tools: differentiating identities
III. Special distributions. Discrete distributions
Continuous random variables: uniform and exponential
Continuous random variables: the normal distribution
The gamma function and related distributions
The chi-square distribution
IV. Limit theorems. Inequalities and laws of large numbers
Stirling's formula
Generating functions and convolutions
Proof of the central limit theorem
Fourier analysis and the central limit theorem
V. Additional topics. Hypothesis testing
Difference equations, Markov processes, and probability
The method of least squares
Two famous problems and some coding

Online version restricted to NUS staff and students only through NUSNET.

For students learning probability, its numerous applications, techniques, and methods can seem intimidating and overwhelming. That's where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course, this accessible and user-friendly study guide helps students comfortably navigate probability's terrain and achieve positive results. The Probability LIfesaver is based on a successful course that Steven Miller has taught at Brown University, Mount Holyoke College, and Williams College. With a relaxed and informal style, Miller presents the math with thorough reviews of prerequisite materials, worked-out problems of varying difficulty, and proofs. He explores a topic first to build intuition, and only after that does he dive into technical details. Coverage of topics is comprehensive, and materials are repeated for reinforcement - both in the guide and on the book's website. An appendix goes over proof techniques, and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus. The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses. -- from back cover

Mode of access: World Wide Web.

System requirements: Internet connectivity; World Wide Web browser.