This online math course develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life.
Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas.
- Probability, Intuition, and Axioms
- Probability by Counting and Inclusion-Exclusion
- Principles of Counting
- Conditional Probability
- Conditional Craps
- Lying Witnesses and Simpson’s Paradox
- Random Variables
- Expectation I
- Expectation II
- Tartan Dice; Terminated Geometric; World Series Pitchers; Negative Hypergeometric; Coin Tossing
- Expected Lead Time; Bijections between Paths
Instructor: Paul G. Bamberg