# Probability, 2ed: An Introduction with Statistical Applications

ISBN: 9788126574278

480 pages

Exclusively distributed by I.K. International

## Description

"This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory." - The Statistician. Thoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, hypothesis testing, and simple linear regression. Encouraging readers to develop a deeper intuitive understanding of probability, the author presents illustrative geometrical presentations and arguments without the need for rigorous mathematical proofs.

Preface for the First Edition

Preface for the Second Edition

1. Sample Spaces and Probability

1.1. Discrete Sample Spaces

1.2. Events; Axioms of Probability

1.3. Probability Theorems

1.4. Conditional Probability and Independence

1.5. Some Examples

1.6. Reliability of Systems

1.7. Counting Techniques

2. Discrete Random Variables and Probability Distributions

2.1. Random Variables

2.2. Distribution Functions

2.3. Expected Values of Discrete Random Variables

2.4. Binomial Distribution

2.5. A Recursion

2.6. Some Statistical Considerations

2.7. Hypothesis Testing: Binomial Random Variables

2.8. Distribution of A Sample Proportion

2.9. Geometric and Negative Binomial Distributions

2.10. The Hypergeometric Random Variable: Acceptance Sampling

2.11. Acceptance Sampling (Continued)

2.12. The Hypergeometric Random Variable: Further Examples

2.13. The Poisson Random Variable

2.14. The Poisson Process

3. Continuous Random Variables and Probability Distributions

3.1. Introduction

3.2. Uniform Distribution

3.3. Exponential Distribution

3.4. Reliability

3.5. Normal Distribution

3.6. Normal Approximation to the Binomial Distribution

3.7. Gamma and Chi-Squared Distributions

3.8. Weibull Distribution

4. Functions of Random Variables; Generating Functions; Statistical Applications

4.1. Introduction

4.2. Some Examples of Functions of Random Variables

4.3. Probability Distributions of Functions of Random Variables

4.4. Sums of Random Variables I

4.5. Generating Functions

4.6. Some Properties of Generating Functions

4.7. Probability Generating Functions for Some Specific Probability Distributions

4.8. Moment Generating Functions

4.9. Properties of Moment Generating Functions

4.10. Sums of Random Variables–II

4.11. The Central Limit Theorem

4.12. Weak Law of Large Numbers

4.13. Sampling Distribution of the Sample Variance

4.14. Hypothesis Tests and Confidence Intervals for a Single Mean

4.16. Least Squares Linear Regression

4.17. Quality Control Chart for X

5. Bivariate Probability Distributions

5.1. Introduction

5.2. Joint and Marginal Distributions

5.3. Conditional Distributions and Densities

5.4. Expected Values and the Correlation Coefficient

5.5. Conditional Expectations

5.6. Bivariate Normal Densities

5.7. Functions of Random Variables

6. Recursions and Markov Chains

6.1. Introduction

6.2. Some Recursions and their Solutions

6.3. Random Walk and Ruin

6.4. Waiting Times for Patterns in Bernoulli Trials

6.5. Markov Chains

7. Some Challenging Problems

7.1. My Socks and √

7.2. Expected Value

7.3. Variance

7.4. Other “Socks” Problems

7.5. Coupon Collection and Related Problems

7.6. Conclusion

7.7. Jackknifed Regression and the Bootstrap

7.8. Cook’s Distance

7.9. The Bootstrap

7.10. On Waldegrave’s Problem

7.11. Probabilities of Winning

7.12. More than Three Players

7.13. Conclusion

7.14. On Huygen’s First Problem

7.15. Changing the Sums for the Players

Bibliography

Appendix A. Use of Mathematica in Probability and Statistics

Appendix B. Answers for Odd-Numbered Exercises

Appendix C. Standard Normal Distribution

Index