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Probability and Mathematical Statistics - 1st Edition - ISBN: 9780124598508, 9781483269207

Probability and Mathematical Statistics

1st Edition

An Introduction

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Author: Eugene Lukacs
eBook ISBN: 9781483269207
Imprint: Academic Press
Published Date: 28th January 1971
Page Count: 254
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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



Part I. Probability Theory

Chapter 1. The Probability Space

1.1 The Outcome Space

1.2 Probabilities

1.3 The Axioms

1.4 Problems


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


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


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


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


Chapter 8. Estimation

8.1 Properties of Estimates

8.2 Point Estimation

8.3 Interval Estimation

8.4 Problems


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


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



No. of pages:
© Academic Press 1972
28th January 1971
Academic Press
eBook ISBN:

About the Author

Eugene Lukacs

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