Probability and Mathematical Statistics
An Introduction
Published on 10. May 2014
254 pages
978-1-4832-6920-7 (ISBN)
Description
Probability and Mathematical Statistics: An Introduction provides a well-balanced first introduction to probability theory and mathematical statistics. This book is organized into two sections encompassing nine chapters. The first part deals with the concept and elementary properties of probability space, and random variables and their probability distributions. This part also considers the principles of limit theorems, the distribution of random variables, and the so-called student's distribution. The second part explores pertinent topics in mathematical statistics, including the concept of sampling, estimation, and hypotheses testing. This book is intended primarily for undergraduate statistics students.
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01/1972
Academic Press
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Content
PrefaceIntroductionPart I. Probability Theory Chapter 1. The Probability Space 1.1 The Outcome Space 1.2 Probabilities 1.3 The Axioms 1.4 Problems References Chapter 2. Elementary Properties of Probability Spaces 2.1 Simple Consequences of the Axioms 2.2 Conditional Probability and Independence 2.3 Finite Probability Spaces 2.4 Problems Chapter 3. Random Variables and Their Probability Distributions 3.1 Random Variables 3.2 Distribution Functions 3.3 Examples of Discrete Distributions 3.4 Examples of Absolutely Continuous Distributions 3.5 Multivariate Distributions 3.6 Problems References Chapter 4. Typical Values 4.1 The Mathematical Expectation of a Random Variable 4.2 Expectations of Functions of Random Variables 4.3 Properties of Expectations 4.4 Moments 4.5 Regression 4.6 Problems Reference Chapter 5. Limit Theorems 5.1 Laws of Large Numbers 5.2 The Central Limit Theorem 5.3 The Poisson Approximation to the Binomial 5.4 Problems References Chapter 6. Some Important Distributions 6.1 The Distribution of the Sum of Independent, Absolutely Continuous Random Variables 6.2 Addition of Independent Normal Random Variables 6.3 The Chi-Square Distribution 6.4 Student's Distribution 6.5 ProblemsPart II. Mathematical Statistics Chapter 7. Sampling 7.1 Statistical Data 7.2 Sample Characteristics 7.3 Moments and Distributions of Sample Characteristics 7.4 Problems References Chapter 8. Estimation 8.1 Properties of Estimates 8.2 Point Estimation 8.3 Interval Estimation 8.4 Problems References Chapter 9. Testing Hypotheses 9.1 Statistical Hypotheses 9.2 The Power of a Test 9.3 The t-Test 9.4 Nonparametric Methods 9.5 Problems ReferencesAppendix A. Some Combinatorial FormulasAppendix B. The Gamma FunctionAppendix C. Proof of the Central Limit TheoremAppendix D. TablesAnswers to Selected ProblemsIndex
