Introduction to Probability with Statistical Applications

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 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.