Introduction to Probability with Statistical Applications
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Beschreibung
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. 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. Topics include random phenomena, discrete and continuous random variables, expectations and variance, and common probability distributions such as the binomial, Poisson, and normal. Combinatorial principles involve all four arithmetic operations. There is an emphasis on tree diagrams. Throughout the book there are references to more advanced concepts that may be safely skipped, depending on the reader.
Theory and applications carefully balanced Presentation is rigorous and contains theorems and proofs Linear algebra is largely avoided Clear definitions, simplified notation and techniques of statistical analysis Well-chosen examples and exercises Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material
Autor*in
Géza Schay
Themen in »Introduction to Probability with Statistical Applications«
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From the reviews:
"The textbook under consideration provides material for approximately a two semester introductory course in probability theory and statistics at the university level, particularly for students with non-mathematical major subjects, such as computer sciences, engineering and other natural and social sciences. It includes seven chapters in about 300 pages covering the most relevant basic fields. … The large amount of exercises, a lot of diagrams and the mnemonic heading of each statement and definition will find a thankful audience for sure." (Michael Högele, Zentralblatt MATH, Vol. 1135 (13), 2008)
"This textbook is a classical and well-written introduction to probability theory and statistics. … the book is written ‘for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.’ … Each new concept is clearly explained and is followed by many detailed examples. … numerous examples of calculations are given and proofs are well-detailed." (Sophie Lemaire, Mathematical Reviews, Issue 2008 m)
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