An Introduction to Probability and Statistical Inference, Second Edition

Probability models, statistical methods, and the information to be gained from them is vital for work in business, engineering, sciences (including social and behavioral), and other fields. Data must be properly collected, analyzed and interpreted in order for the results to be used with confidence. Award-winning author George Roussas introduces readers with no prior knowledge in probability or statistics to a thinking process to guide them toward the best solution to a posed question or situation. An Introduction to Probability and Statistical Inference provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. 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 activities Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding A 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 disciplines Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual 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 activities Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding A 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 disciplines Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual Probability models, statistical methods, and the information to be gained from them is vital for work in business, engineering, sciences (including social and behavioral), and other fields. Data must be properly collected, analyzed and interpreted in order for the results to be used with confidence.

Award-winning author George Roussas introduces readers with no prior knowledge in probability or statistics to a thinking process to guide them toward the best solution to a posed question or situation. An Introduction to Probability and Statistical Inference provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations.

• 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 activities
• Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding
• A 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 disciplines
• Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions
• Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual

Content: Inside Front Matter, Pages ES2-ES3 Front Matter, Pages i-ii Copyright, Page iv Dedication, Page v Preface, Pages xi-xiv Chapter 1 - Some motivating examples and some fundamental concepts, Pages 1-22 Chapter 2 - The concept of probability and basic results, Pages 23-76 Chapter 3 - Numerical characteristics of a random variable, some special random variables, Pages 77-133 Chapter 4 - Joint and conditional p.d.f.’s, conditional expectation and variance, moment generating function, covariance, and correlation coefficient, Pages 135-186 Chapter 5 - Independence of random variables and some applications, Pages 187-206 Chapter 6 - Transformation of random variables, Pages 207-243 Chapter 7 - Some modes of convergence of random variables, applications, Pages 245-271 Chapter 8 - An overview of statistical inference, Pages 273-285 Chapter 9 - Point estimation, Pages 287-328 Chapter 10 - Confidence intervals and confidence regions, Pages 329-347 Chapter 11 - Testing hypotheses, Pages 349-395 Chapter 12 - More about testing hypotheses, Pages 397-418 Chapter 13 - A simple linear regression model, Pages 419-452 Chapter 14 - Two models of analysis of variance, Pages 453-484 Chapter 15 - Some topics in nonparametric inference, Pages 485-515 Tables, Pages 517-550 Some notation and abbreviations, Pages 551-553 Answers to even-numbered exercises, Pages 555-598 Index, Pages 599-606 Inside Back Matter, Page ES4 Some motivating examples and some fundamental concepts -- The concept of probability and some basic results -- Numerical characteristics of a random variable, some special random variables -- Joint and conditional P.D.F.'s, conditional expectation and variance, moment generating function, covariance and correlation coefficient -- Independence of random variables and some applications -- Transformation of random variables -- Some modes of convergence of random variables, applications -- An overview of statistical inference -- Point estimation -- Confidence intervals and confidence regions -- Testing hypotheses -- More about testing hypotheses -- A simple linear regression model -- Two models of analysis of variance -- Some topics in nonparametric inference