Introduction to probability theory and its applications. Combinatorial analysis, axioms of probability and independence, random variables (discrete and continuous), joint probability distributions, properties of expectation, Central Limit Theorem, Law of Large Numbers, Markov chains.

HOURS: 9:50- 11:25; Tu. and Th.
ROOM: ONLINE

### Instructor

Bruno Sansó, E2 525

OFFICE HOURS: Tue - Thu 1:30 - 2:30

### Teaching Assistants

• Yunzhe Li, PhD student in Statistical Sciences
• Xiaotian Zheng, PhD student in Statistical Sciences

### General Informtion

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.

Textbook: (required)

• 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.