This text combines the topics generally found in main-stream elementary statistics books with the essentials of the underlying theory. The book begins with an axiomatic treatment of probability followed by chapters on discrete and continuous random variables and their associated distributions. It then introduces basic statistical concepts including summarizing data and interval parameter estimation, stressing the connection between probability and statistics. Final chapters introduce hypothesis testing, regression, and non-parametric techniques. All chapters provide a balance between conceptual understanding and theoretical understanding of the topics at hand.

Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Knowledge updating is a never-ending process and so should be the revision of an effective textbook. The book originally written fifty years ago has, during the intervening period, been revised and reprinted several times. The authors have, however, been thinking, for the last few years that the book needed not only a thorough revision but rather a substantial rewriting. They now take great pleasure in presenting to the readers the twelfth, thoroughly revised and enlarged, Golden Jubilee edition of the book. The subject-matter in the entire book has been re-written in the light of numerous criticisms and suggestions received from the users of the earlier editions in India and abroad. The basis of this revision has been the emergence of new literature on the subject, the constructive feedback from students and teaching fraternity, as well as those changes that have been made in the syllabi and/or the pattern of examination papers of numerous universities. Some prominent additions are given below: 1. Variance of Degenerate Random Variable 2. Approximate Expression for Expectation and Variance 3. Lyapounov’s Inequality 4. Holder’s Inequality 5. Minkowski’s Inequality 6. Double Expectation Rule or Double-E Rule and many others

This textbook introduces the mathematical concepts and methods that underlie statistics. The course is unified, in the sense that no prior knowledge of probability theory is assumed, being developed as needed. The book is committed to both a high level of mathematical seriousness and to an intimate connection with application. In its teaching style, the book is * mathematically complete * concrete * constructive * active. The text is aimed at the upper undergraduate or the beginning Masters program level. It assumes the usual two-year college mathematics sequence, including an introduction to multiple integrals, matrix algebra, and infinite series.

This book gives an introduction into mathematical statistics.

Fundamentals of Mathematical Statistics is meant for a standard one-semester advanced undergraduate or graduate-level course in Mathematical Statistics. It covers all the key topics—statistical models, linear normal models, exponential families, estimation, asymptotics of maximum likelihood, significance testing, and models for tables of counts. It assumes a good background in mathematical analysis, linear algebra, and probability but includes an appendix with basic results from these areas. Throughout the text, there are numerous examples and graduated exercises that illustrate the topics covered, rendering the book suitable for teaching or self-study. Features A concise yet rigorous introduction to a one-semester course in Mathematical Statistics Covers all the key topics Assumes a solid background in Mathematics and Probability Numerous examples illustrate the topics Many exercises enhance understanding of the material and enable course use This textbook will be a perfect fit for an advanced course in Mathematical Statistics or Statistical Theory. The concise and lucid approach means it could also serve as a good alternative, or supplement, to existing texts.