Probability for Statisticians This 2nd edition textbook offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians a textbook for courses in probability for students in mathematical statistics. It is recommended to anyone interested in the probability underlying modern statistics providing a solid grounding in the probabilistic tools and techniques necessary to do theoretical research in statistics. For the teaching of probability theory to post graduate statistics students this is one of the most attractive books available. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. Martingale coverage includes coverage of censored data martingales. The text includes measure theoretic preliminaries from which the authors own course typically includes selected coverage. This is a heavily reworked and considerably shortened version of the first edition of this textbook. Extra and background material has been either removed or moved to the appendices and important rearrangement of chapters has taken place to facilitate this books intended use as a textbook. New to this edition: Still up front and central in the book Chapters 1 5 provide the measure theory necessary for the rest of the textbook and Chapters 6 7 adapt that measure theoretic background to the special needs of probability theory Develops both mathematical tools and specialized probabilistic tools Chapters organized by number of lectures to cover requisite topics optional lectures and self study Exercises interspersed within the text Guidance provided to instructors to help in choosing topics of emphasis Preface Use of This Text Definition of Symbols Chapter 1. Measures Chapter 2. Measurable Functions and Convergence Chapter 3. Integration Chapter 4 Derivatives via Signed Measures Chapter 5. Measures and Processes on Products Chapter 6. Distribution and Quantile Functions Chapter 7. Independence and Conditional Distributions Chapter 8. WLLN SLLN LIL and Series Chapter 9. Characteristic Functions and Determining Classes Chapter 10. CLTs via Characteristic Functions Chapter 11. Infinitely Divisible and Stable Distributions Chapter 12. Brownian Motion and Empirical Processes Chapter 13. Martingales Chapter 14. Convergence in Law on Metric Spaces Chapter 15. Asymptotics Via Empirical Processes Appendix A. Special Distributions Appendix B. General Topology and Hilbert Space Appendix C. More WLLN and CLT References Index