PROBABILITY

Course Description

The intention of the course is for students to learn the main tools and techniques of modern probability theory in a form that is accessible. Only a background in calculus and linear algebra is assumed. Basic concepts from set theory and real analysis required to introduce measure theoretic probability are covered. Beginning with Kolmogorov’s probability axioms we build a model for randomness, formalizing the notion of a random variable as a function and the expectation of a random variable as an integral. We then study the convergence of sequences of random variables and their expectations to solve a number of classic problems in probability theory involving random walks, urn models, gambling strategies, etc.

Required Text

Sheldon Ross, Introduction to Probability Models, 10th or 11th edition, AP

Optional Text

1. Saeed Ghahramani, Fundamentals of Probability with Stochastic Processes 3d Edition or Later, Routledge

2. Sidney Resnick, A Probability Path Birkhauser

3. Robert P. Dobrow, Introduction to Stochastic Processes with R, John Wiley & Sons Inc.