We will cover following topics (cf. also schedule below):
Chapter 1. Review of Discrete and Continuous Probability.
Chapter 2. Conditional Expectation.
Chapter 3. Moment Generating Functions.
Chapter 4. Tail Bounds & Limit Theorems.
Chapter 5. Random Walk.
Chapter 6. Markov Chains.
Chapter 7. Introduction to Martingales.
Homework: There will be 7 Homework assignments. Homework problems will be posted every Monday on Gauchospace and will be submitted on Gauchospace on Friday one week later at 11:59 p.m.. No late homework submission will be accepted! Three problems will be graded by your TA. Graded homework will be discussed during the sections. Homework will count for final grade (see below). The lowest homework grade will be dropped.
Python Homework: There will be 6 Python Homework assignments. Python problem sheets in the format of Jupyter Notebooks will be posted every Friday on Gauchospace and will be due on Friday two weeks later at 11:59 p.m. They will be submitted via GauchoSpace. Please submit
your pdf file and your jupyter notebook file (.ipynb) with all coding and results. Please give yourself enough time to submit your work.