Introduction to Probability

• Contents
• Preface
• Probability and Events
• Assumptions for probability, and their consequences
• Models with continuous sample spaces
• Conditional probability
• Independence and its consequences
• Tricky little problems
• Independent sequences
• Counting
• Random variables
• Expected values, finite range case
• More properties of expected value
• Independent random variables, first applications
• Waiting times
• Random variables with countable range
• Exponential waiting times
• Moments and inequalities
• Poisson random variables
• Normal random variables and the Central Limit Theorem
• Appendices
• Bibliography
• Index

This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons which underlie the rules of probability are emphasized. Probability theory is certainly useful. But how does it feel to study it? Well, like other areas of mathematics, probability theory contains elegant concepts, and it gives you a chance to exercise your ingenuity, which is often fun. But in addition, randomness and probability are part of our experience in the real world, present everywhere and yet still somewhat mysterious. This gives the subject of probability a special interest.