Introduction to Probability with Statistical Applications

✍ Scribed by Geza Schay

• Publisher: Birkhäuser Boston
• Year: 2007
• Tongue: English
• Leaves: 316
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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