This text focuses on the utility of probability in solving real-world problems for students in a one-semester calculus-based probability course. Theory is developed to a practical degree and grounded in discussion of its practical uses in solving real-world problems. Numerous applications using up-to-date real data in engineering and the life, social, and physical sciences illustrate and motivate the many ways probability affects our lives. The text’s accessible presentation carefully progresses from routine to more difficult problems to suit students of different backgrounds, and carefully explains how and where to apply methods. Students going on to more advanced courses in probability and statistics will gain a solid background in fundamental concepts and theory, while students who must apply probability to their courses engineering and the sciences will develop a working knowledge of the subject and appreciation of its practical power.
1. Probability in the World Around Us
2. Foundations of Probability
3. Conditional Probability and Independence
4. Discrete Probability Distributons
5. Continuous Probability Distributions
6. Multivariate Probability Distributions
7. Functions of Random Variables
8. Some Approximations to Probability Distributions: Limit Theorems
9. Extensions of Probability Theory