Book description
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
Table of contents
- Cover image
- Title page
- Table of Contents
- Inside Front Matter
- Copyright
- Dedication
- Preface
- Chapter 1: Some motivating examples and some fundamental concepts
- Chapter 2: The concept of probability and 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
- 4.1 Joint D.F. and Joint p.d.f. of Two Random Variables
- 4.2 Marginal and Conditional p.d.f.'s, Conditional Expectation and Variance
- 4.3 Expectation of a Function of Two r.v.'s, Joint and Marginal m.g.f.'s, Covariance, and Correlation Coefficient
- 4.4 Some Generalizations to k Random Variables
- 4.5 The Multinomial, the Bivariate Normal, and the Multivariate Normal Distributions
- 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
- 13.1 Setting up The Model—The Principle of Least Squares
- 13.2 The Least Squares Estimates of β1 and β2 and Some of Their Properties
- 13.3 Normally Distributed Errors: MLE's of β1, β2, and σ2, Some Distributional Results
- 13.4 Confidence Intervals and Hypotheses Testing Problems
- 13.5 Some Prediction Problems
- 13.6 Proof of Theorem 5
- 13.7 Concluding Remarks
- Chapter 14: Two models of analysis of variance
- Chapter 15: Some topics in nonparametric inference
- Tables
- Some notation and abbreviations
- Answers to even-numbered exercises
- Index
- Inside Back Matter
Product information
- Title: An Introduction to Probability and Statistical Inference, 2nd Edition
- Author(s):
- Release date: October 2014
- Publisher(s): Academic Press
- ISBN: 9780128004371
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