Instructor: Dimitrios Katselis, Email: katselis@illinois.edu
TAs: Yicheng Sun, Yijin Wang Emails: {yicheng9, yijinw3}@illinois.edu
Schedule: MW 11am-12:20pm, ECEB 1015
Office Hours : Yicheng: Fri, 2-3pm, zoom Yijin: Tue, 10-11am , zoom Dimitris: W 3-4pm, zoom
Syllabus: Text, notes and grading are as in the syllabus of Spring 2020 below. Links to text and notes are also provided there
Submissions via gradescope
Lectures are heavily based on the notes by Prof. Srikant and the text by Prof. Hajek (Spring 2020 syllabus).
For in-class notes, please contact Yicheng.
Disclaimer: The in-class notes correspond to files shared by your classmates. Therefore, no correction of typos or of technical
parts will be performed. It is highly suggested that you attend lectures, take your own notes and use the posted in-class notes as
complementary material.
| Week 1 | Probability Space | Lecture 1 by Prof. Srikant, Section 1.1 by Prof. Hajek |
| Week 2 | Probability Space, Conditional Probability and Independence, Measurability | Lecture 2 by Prof. Srikant, Sections 1.1, 1.2 by Prof. Hajek |
| Week 3 | Basic Inequalities (Markov, Reverse Markov and Chebyshev), Fundamental Functions, Important Distributions | Lectures 3,4 by Prof. Srikant, Sections 1.5, 1.6 by Prof. Hajek |
| Week 4 | Important Distributions, Jointly Distributed Random Variables, Functions of Random Variables, Jensen's Inequality | Lectures 4-7 by Prof. Srikant, Sections 1.6, 1.8-1.11, 2.4 by Prof. Hajek |
| Week 5 | Jensen's Inequality, Gaussian Tail and Chernoff Bounds, CLT, Hoeffding Bound | Lectures 7-9 by Prof. Srikant, Sections 2.3-2.5 by Prof. Hajek |
| Week 6 | Hoeffding Bound, Change of Measure, Convergence of Sequences of Random Variables | Lecture 11 by Prof. Srikant, Sections 2.1 by Prof. Hajek |
| Weeks 7-9 | Convergence of Sequences of Random Variables, Cauchy Criteria, Skorokhod's Representation Theorem, LLN, Borel-Cantelli Lemma, Monotone Covnergence | Lecture 10 by Prof. Srikant, Sections 1.2, 2.2 by Prof. Hajek |
| Week 10 | SLLN, MMSE and LMMSE Estimation | Lecture 12 by Prof. Srikant, Sections 3.1-3.3 by Prof. Hajek |
| Week 11 | Jointly Gaussian Random Variables | Lecture 13 by Prof. Srikant, Section 3.4 by Prof. Hajek |
| Weeks 12-14 | DTMCs, Martingales, Poisson Process, Brownian Motion, Stationarity, Ergodicity, WSS, Wiener and Kalman Filtering | Lectures 14, 17, 18, 20-26 by Prof. Srikant, Sections 3.5-3.6, 4,3-4.7, 6.1-6.2, 7.4, 8.1-8.3 by Prof. Hajek |
| Midterm 1 | March 8 | in class | |
| Midterm 2 | April 12 | in class | |
| Final | May 11, 8-11am | ECEB 1015 |