Introduction to Probability with Statistical Applications

I am a PhD student in Computer Science at UMass Boston and I do research in data mining. I am particularly interested in probabilistic solutions to problems in data mining, which is why I wanted to know about probability and statistics. I had the privilege of learning the subject matter from the author (Prof. Schay) himself. I learned a lot, both from this excellent text, and from Prof. Schay's clear in-class explanations of the topics. This is a wonderful book for students learning probability and statistics for the first time. It offers an easy-to-understand and yet rigorous treatment of the subject matter. The book also offers a lot for the more experienced students. Chapter 1 introduces the algebra of events. Chapter 2 offers a very lucid explanation of combinatorial principles. Chapter 3 provides a good introduction to probability, including descriptions of the axioms of probability, independence, conditional probabilities, and the theorems of total probability and Bayes. Chapter 4 offers an excellent description of Random Variables (RVs), with clear explanations of probability and distribution functions, continuous RVs, functions of RVs, joint distributions, independence of RVs, and conditional distributions. Chapter 5 provides an introduction to statistics. Chapter 6 provides descriptions of some special distributions, such as, Poisson distribution, Normal distribution, etc. Finally, chapter 7 addresses some of the advanced topics in statistics, such as, estimation, testing hypotheses, power function of a test, sampling from normally distributed populations, etc. The main highlight of the book is that each chapter is divided into fairly small sections; each section explains a single concept through numerous examples, and includes several exercises at the end, so a student can thoroughly understand the material of a section before moving on to the next. The book, at the end, includes answers and hints to selected odd-numbered exercises. I highly recommend this text to students interested in learning probability and statistics. Swami This textbook is an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. Main statistical concepts considered are point and interval estimates, hypothesis testing, power function, various statistical tests: z, t, chi-squareand Kolmogorov-Smirnov. Key features: @* Presents rigorous discussion, with definitions, theorems, and proofs, but aimed at a non-specialist audience; @*Avoids linear algebra; @* Treats informally the few unavoidable concepts from multivariable calculus, such as double integrals; @* Motivates new concepts throughout using examples and brief conceptual discussions; @* Develops basic ideas with clear definitions, carefully designed notation and techniques of statistical analysis, along with well-chosen examples, exercises and applications. The book contains enough material for two semesters but, with judicious selection, it can also be used for a one-semester course, either in probability and statistics or in probability alone. .Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications This textbook is an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. Main statistical concepts considered are point and interval estimates, hypothesis testing, power function, various statistical tests: z, t, chi-square and Kolmogorov-Smirnov. Key features: * Presents rigorous discussion, with definitions, theorems, and proofs, but aimed at a non-specialist audience; *Avoids linear algebra; * Treats informally the few unavoidable concepts from multivariable calculus, such as double integrals; * Motivates new concepts throughout using examples and brief conceptual discussions; * Develops basic ideas with clear definitions, carefully designed notation and techniques of statistical analysis, along with well-chosen examples, exercises and applications. The book contains enough material for two semesters but, with judicious selection, it can also be used for a one-semester course, either in probability and statistics or in probability alone. .Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications. Introduction to Probability with Statistical Applications targets non-mathematics students, undergraduates and graduates, who do not need an exhaustive treatment of the subject. While the presentation is rigorous and contains theorems and proofs, linear algebra is largely avoided and only a minimal amount of multivariable calculus is needed. Key features:Clear definitions, simplified notation and techniques of statistical analysis, combined with well-chosen examples and exercises, motivate the expositionTheory and applications carefully balancedTopics include random phenomena -- discrete and continuous random variables -- expectations and variance, and common probability distributions such as the binomial, Poisson, and normalCombinatorial principles involve all four arithmetic operations; emphasis on tree diagramsReferences to more advanced concepts throughout the book, but may be safely skipped, depending on the reader For students in a variety of disciplines, including computer science, engineering, natural and social sciences. Cover......Page 1 Introduction to Probability with Statistical Applications......Page 3 Preface......Page 5 Contents......Page 8 Introduction......Page 10 1 The Algebra of Events......Page 12 2 Combinatorial Problems......Page 23 3 Probabilities......Page 44 4 Random Variables......Page 78 5 Expectation, Variance, Moments......Page 133 6 Some Special Distributions......Page 182 7 The Elements of Mathematical Statistics......Page 226 Appendix I: Tables......Page 281 Table 1. Standard normal d.f.......Page 282 Table 2. Percentiles of the t distribution......Page 283 Table 3. Percentiles of the χ2 distribution......Page 284 Table 4. One-Sample Kolmogorov-Smirnov Test......Page 285 Table 5. Critical Values for the Two-Sample Kolmogorov–Smirnov Statistic......Page 286 Appendix II: Answers and Hints for Selected Odd-Numbered Exercises......Page 287 References......Page 311 Index......Page 312 Introduction to Probability with Statistical Applications targets non-mathematics students, undergraduates and graduates, who do not need an exhaustive treatment of the subject. The presentation is rigorous and contains theorems and proofs, and linear algebra is largely avoided so only a minimal amount of multivariable calculus is needed. The book contains clear definitions, simplified notation and techniques of statistical analysis, which combined with well-chosen examples and exercises, motivate the exposition. Theory and applications are carefully balanced. Throughout the book there are references to more advanced concepts if required. "This textbook is an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The book contains enough material for two semesters but, with judicious selection, it can also be used for a one-semester course, either in probability and statistics or in probability alone. Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications."--Jacket Designed for non-mathematics students, undergraduate and graduates, who do not need an exhaustive treatment of statistics. While the presentation is rigorous and contains theorems and proofs, linear algebra is largely avoided and only a minimal amount of multivariable calculus is needed