First Course in Probability, A: International Edition (8e)

A First Course in Probability, Eighth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.

1. Combinatorial Analysis

2. Axioms of Probability

3. Conditional Probability and Independence

4. Random Variables

5. Continuous Random Variables

6. Jointly Distributed Random Variables

7. Properties of Expectation

8. Limit Theorems

9. Additional Topics in Probability

10. Simulation

Appendix A. Answers to Selected Problems

Appendix B. Solutions to Self-Test Problems and Exercises

Index

• New problems, exercises, and text materials maintain student interest and build intuition about probability.
• Coverage of the important result that the expectation of a sum of random variables is equal to the sum of the expectations now occurs in Chapter 4 (Random Variables). A new and elementary proof of this result when the sample space of the probability experiment is finite is also given in this chapter.
• Section 6.3, which deals with the sum of independent random variables, has been expanded.
• A new section 6.3.1 derives the distribution of the sum of independent and identically distributed uniform random variables. This section also demonstrates that the expected number of random numbers that need to be added for their sum to exceed 1 is equal to e.
• Section 6.3.5 has been added to derive the distribution of the sum of independent geometric random variables with different means.

• Intuitive explanations are supported with an abundance of examples to give readers a thorough introduction to this complex topic.
• Analysis is unique to the text and elegantly designed. Examples include the knockout tournament and multiple players gambling ruin problem, as well as the new results concerning the sum of uniform and the sum of geometric random variables.
• Three sets of exercises are given at the end of each chapter. These include Problems, Theoretical Exercises, and Self-Test Problems and Exercises. The Self-Test Problems and Exercises include complete solutions in the appendix, allowing students to test their comprehension and study for exams.

Sheldon M. Ross is a professor in the Department of Industrial Engineering and Operations Research at the University of Southern California. He received his Ph.D. in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences, the Advisory Editor for International Journal of Quality Technology and Quantitative Management, and an Editorial Board Member of the Journal of Bond Trading and Management.  He is a Fellow of the Institute of Mathematical Statistics and a recipient of the Humboldt US Senior Scientist Award.