Springer, 2010.
Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the exteal world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-first century, as difficult new problems emerge, that will require more sophisticated models and analysis.
This is a text on the fundamentals of the theory of probability at an undergraduate or first-year graduate level for students in science, engineering, and economics. The only mathematical background required is knowledge of univariate and multivariate calculus and basic linear algebra. The book covers all of the standard topics
in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random variables. But it also has some unique features and a forwardlooking feel. Some unique features of this book are its emphasis on conceptual discussions, a lively writing style, and on presenting a large variety of unusual and interesting examples; careful and more detailed treatment of normal and Poisson approximations (Chapters 6 and 10); better exposure to distribution theory, including developing superior skills in working with joint and conditional distributions and the bivariate normal distribution (Chapters 11, 12, and 13); a complete and readable account of finite Markov chains (Chapter 14); treatment of mode u models and statistical genetics (Chapter 15); special efforts to make the book user-friendly, with unusually detailed chapter summaries, and a unified collection of formulas from the text, and from algebra, trigonometry, geometry, and calculus in the appendix of the book, for immediate and easy reference; and use of interesting Use Your Computer simulation projects as part of the chapter exercises to help students see a theoretical result evolve in their own computer work.
The exercise sets form a principal asset of this text. They contain a wide mix of problems at different degrees of difficulty. While many are straightforward, many others are challenging and require a student to think hard. These harder problems are always marked with an asterisk. The chapter ending exercises that are not marked with an asterisk generally require only straightforward skills, and these are also essential for giving a student confidence in problem solving. The book also gives a set of supplementary exercises for additional homework and exam preparation. The supplementary problem set has 185 word problems and a very carefully designed set of 120 true/false problems. Instructors can use the true/false problems to encourage students to lea to think and also quite possibly for weekly homework. The total number of problems in the book is 810.
Probability theory is one branch of mathematics that is simultaneously deep and immediately applicable in diverse areas of human endeavor. It is as fundamental as calculus. Calculus explains the exteal world, and probability theory helps predict a lot of it. In addition, problems in probability theory have an innate appeal, and the answers are often structured and strikingly beautiful. A solid background in probability theory and probability models will become increasingly more useful in the twenty-first century, as difficult new problems emerge, that will require more sophisticated models and analysis.
This is a text on the fundamentals of the theory of probability at an undergraduate or first-year graduate level for students in science, engineering, and economics. The only mathematical background required is knowledge of univariate and multivariate calculus and basic linear algebra. The book covers all of the standard topics
in basic probability, such as combinatorial probability, discrete and continuous distributions, moment generating functions, fundamental probability inequalities, the central limit theorem, and joint and conditional distributions of discrete and continuous random variables. But it also has some unique features and a forwardlooking feel. Some unique features of this book are its emphasis on conceptual discussions, a lively writing style, and on presenting a large variety of unusual and interesting examples; careful and more detailed treatment of normal and Poisson approximations (Chapters 6 and 10); better exposure to distribution theory, including developing superior skills in working with joint and conditional distributions and the bivariate normal distribution (Chapters 11, 12, and 13); a complete and readable account of finite Markov chains (Chapter 14); treatment of mode u models and statistical genetics (Chapter 15); special efforts to make the book user-friendly, with unusually detailed chapter summaries, and a unified collection of formulas from the text, and from algebra, trigonometry, geometry, and calculus in the appendix of the book, for immediate and easy reference; and use of interesting Use Your Computer simulation projects as part of the chapter exercises to help students see a theoretical result evolve in their own computer work.
The exercise sets form a principal asset of this text. They contain a wide mix of problems at different degrees of difficulty. While many are straightforward, many others are challenging and require a student to think hard. These harder problems are always marked with an asterisk. The chapter ending exercises that are not marked with an asterisk generally require only straightforward skills, and these are also essential for giving a student confidence in problem solving. The book also gives a set of supplementary exercises for additional homework and exam preparation. The supplementary problem set has 185 word problems and a very carefully designed set of 120 true/false problems. Instructors can use the true/false problems to encourage students to lea to think and also quite possibly for weekly homework. The total number of problems in the book is 810.