This course consists of an introduction to probability theory and its applications. The main goal is to develop the basic mathematical tools to consider models that incorporate uncertainty using a probabilistic framework. We start by introducing the axioms of probability and the rules needed to perform calculations with probabilities. We then move into the concepts of independence, conditional probability and Bayes theory, define a random variable, both discrete and continuous, and consider its probability distribution function as well as its expectation and higher order moments. We extend these ideas to the multivariate case. Finally we consider some more advanced topics like the Law of Large Numbers, Central Limit theorem and, time permitting, a brief introduction to some simple stochastic processes like Markov Chains and Poisson Processes.
It is assumed that students have a good working knowledge of multivariate calculus.
M.H. DeGroot and M.J. Schervish (2002) Probability and Statistics. Fourth Edition (if you have the third edition that's fine too). Addison Wesley.
Additional Reference: A First Course in Probability (sixth edition). S. Ross. Prentice Hall
Quiz 1: 10/13/15 11:00 - 11:45. Will include up to the material covered in the 10/06/15 class; Quiz 2: 11/17/15 11:00 - 11:45; Quiz 3: 12/03/15 11:00 - 11:45. Midterm: 10/29/15 10:00 - 11:45 Final: 12/07/15 9:00 - 11:00 Notice that this is a two hour final.
Homework: There will be several (possibly weekly) homework assignments which will not be graded. Homeworks will give you a very close indication of the material that will be covered in exams and quizzes. Some homework will be reviewed in the sections.