The probability lifesaver : all the tools you need to understand chance /
Steven J. Miller.
- xxiii, 727 pages : illustrations ; 26 cm.
- A Princeton lifesaver study guide .
Includes bibliographical references (pages 717-719) and index.
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.
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.
College of Education Bachelor of Secondary Education major in Mathematics