Probability: An Introduction with Statistical Applications

Praise for the First Edition "This is a well–written and impressively presented introduction to probability and statistics.  The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory."  – The Statistician Thoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition is a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an accessible introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, hypothesis testing, and simple linear regression. Encouraging students to develop a deeper intuitive understanding of probability, the author presents illustrative geometrical presentations and arguments without the need for rigorous mathematical proofs. The Second Edition features interesting and practical examples from a variety of engineering and scientific fields as well as: Over 880 problems at varying degrees of difficulty allowing readers to take on more challenging problems as their skill levels increase Chapter–by–chapter projects that aid in the visualization of probability distributions New coverage  of statistical quality control and quality production An appendix dedicated to the use of Mathematica and a companion website containing the referenced data sets Featuring a practical and real–world approach, this textbook is ideal for a first course in probability for students majoring in statistics, engineering, business, psychology, operations research, and mathematics. Probability: An Introduction with Statistical Applications, Second Edition is also an excellent reference for researchers and professionals of any discipline who need to make decisions based on data as well as readers interested in learning how to accomplish effective decision making from data. John J. Kinney, PhD, is Professor Emeritus of Mathematics at Rose–Hulman Institute of Technology in Terre Haute, Indiana. A Member of the American Statistical Association and the Colorado Council of Teachers of Mathematics, Dr. Kinney is the author of numerous journal articles and three books, including A Probability and Statistics Companion , also published by Wiley.

Chapter 1 –  Sample Spaces and Random Variables 1.1 Discrete  Sample Spaces 1.2 Events: Axioms of Probability 1.3 Probability Theorems 1.4 Conditional Probability and Independence 1.5 Some Examples 1.6 Reliability of Systems 1.7 Counting Techniques Chapter Review Problems for Review Supplementary Exercises for Chapter 1 Chapter 2 –  Discrete Random Variables and Probability Distributions 2.1 Random Variables 2.2 Distribution Functions 2.3 Expected Values of Discrete Random Variables 2.4 Binomial Distribution 2.5 A Recursion 2.6 Some Statistical Considerations 2.7 Hypothesis Testing: Binomial Random Variables 2.8 Distribution of a Sample Proportion 2.9 Geometric and Negative Binomial Distributions 2.10 The Hypergeometric Random Variable;  Acceptance Sampling 2.11 Acceptance Sampling (Continued) 2.12 The Hypergeometric Random Variable; Further Examples 2.13 The Poisson Random Variable 2.14 The Poisson Process Chapter Review Problems for Review Supplementary Exercises for Chapter 2 Chapter 3 – Continuous Random Variables and Probability Distributions 3.1 Introduction 3.2 Uniform Distribution 3.3 Exponential Distribution 3.4 Reliability 3.5 Normal Distribution 3.6 Normal Approximation to the Binomial Distribution 3.7 Gamma and Chi–Squared Distributions 3.8 Weibull Distribution Chapter Review Problems for Review Supplementary Exercises for Chapter 3 Chapter 4 – Functions of Random Variables, Generating Functions, and Statistical Applications 4.1 Introduction 4.2 Some Examples of Functions of Random Variables 4.3 Probability Distributions of Functions of Random Variables 4.4 Sums of Random Variables I 4.5 Generating Functions 4.6 Some Properties of Generating Functions 4.7 Probability Generating Functions for Some Specific Probability Distributions 4.8 Moment Generating Functions 4.9 Properties of Moment Generating Functions 4.10 Sums of Random Variables II 4.11 The Central Limit Theorem 4.12 Weak Law of Large Numbers 4.13 Sampling Distribution of the Sample Variance 4.14 Hypothesis Tests and Confidence Intervals for a Single Mean 4.15 Hypothesis Tests on Two Samples 4.16 Least Squares Linear Regression 4.17 Quality Control Chart for X Bar Chapter Review Problems for Review Supplementary Exercises for Chapter 4 Chapter 5 – Bivariate Probability Distributions 5.1 Introduction 5.2 Joint and Marginal Distributions 5.3 Conditional Distributions and Densities 5.4 Expected Values and the Correlation Coefficient 5.5 Conditional Expectations 5.6 Bivariate Normal Densities 5.7 Functions of Random Variables Chapter Review Problems for Review Supplementary Exercises for Chapter 5 Chapter 6 – Recursions and Markov Chains 6.1 Introduction 6.2 Some Recursions and Their Solutions 6.3 Random Walk and Ruin 6.4 Waiting Times for Patterns in Bernoulli Trials 6.5 Markov Chains Chapter Review Problems for Review Supplementary Exercises for Chapter 6 Chapter 7 – Some Challenging Problems 7.1 My Socks and √π 7.2 Coupon Collectors Problems 7.3 The Jackknife and the Bootstrap 7.4 On a Problem of Waldegrave 7.5 On a Problem of Huygens Bibliography Appendix 1 – Use of Mathematica in Probability and Statistics Appendix 2 – Answers to Odd–Numbered Problems Appendix 3 – Tables Index

John J. Kinney, PhD, is Professor Emeritus of Mathematics at Rose–Hulman Institute of Technology in Terre Haute, Indiana. A Member of the American Statistical Association and the Colorado Council of Teachers of Mathematics, Dr. Kinney is the author of numerous journal articles and three books, including A Probability and Statistics Companion , also published by Wiley.