An Introduction to Probability and Statistical Inference

An Introduction to Probability and Statistical Inference, Second Edition, guides you through probability models and statistical methods and helps you to think critically about various concepts. Written by award-winning author George Roussas, this book introduces readers with no prior knowledge in probability or statistics to a thinking process to help them obtain the best solution to a posed question or situation. It provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations.

This text contains an enhanced number of exercises and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities. Reorganized material is included in the statistical portion of the book to ensure continuity and enhance understanding. Each section includes relevant proofs where appropriate, followed by exercises with useful clues to their solutions. Furthermore, there are brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises are available to instructors in an Answers Manual.

This text will appeal to advanced undergraduate and graduate students, as well as researchers and practitioners in engineering, business, social sciences or agriculture.

Content, examples, an enhanced number of exercises, and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activitiesReorganized material in the statistical portion of the book to ensure continuity and enhance understandingA relatively rigorous, yet accessible and always within the prescribed prerequisites, mathematical discussion of probability theory and statistical inference important to students in a broad variety of disciplinesRelevant proofs where appropriate in each section, followed by exercises with useful clues to their solutionsBrief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual

Chapter 1 Some Motivating Examples and Some Fundamental Concepts Chapter 2 The Concept of Probability and Some Basic Results Chapter 3 Numerical Characteristics of a Random Variable, Some Special Random Variables Chapter 4 Joint and Conditional p.d.f.'s, Conditional Expectation and Variance, Moment Generating Function, Covariance and Correlation Coefficient Chapter 5 Independence of Random Variables and Some Applications Chapter 6 Transformation of Random Variables Chapter 7 Some Modes of Convergence of Random Variables, Applications Chapter 8 An Overview of Statistical Inference Chapter 9 Point Estimation Chapter 10 Confidence Intervals and Confidence Regions Chapter 11 Testing Hypotheses Chapter 12 More About Testing Hypotheses Chapter 13 A Simple Linear Regression Model Chapter 14 Two Analysis of Variance Models Chapter 15 Some Topics in Nonparametric Inference