Probability and Mathematical Statistics

Probability and Mathematical Statistics

An Introduction

1st Edition - January 28, 1971

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  • Author: Eugene Lukacs
  • eBook ISBN: 9781483269207

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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.

Table of Contents


  • Preface

    Introduction

    Part 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 Problems

    Part 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

    References

    Appendix A. Some Combinatorial Formulas

    Appendix B. The Gamma Function

    Appendix C. Proof of the Central Limit Theorem

    Appendix D. Tables

    Answers to Selected Problems

    Index

Product details

  • No. of pages: 254
  • Language: English
  • Copyright: © Academic Press 1971
  • Published: January 28, 1971
  • Imprint: Academic Press
  • eBook ISBN: 9781483269207

About the Author

Eugene Lukacs

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