Instructor: Dimitrios Katselis, Email: katselis@illinois.edu
TAs: Yixuan Wang, Yicheng Sun, Emails: {yixuan22,yicheng9}@illinois.edu
Schedule: TR 9:30-10:50am, ECEB 3017
Office Hours : Yixuan: Wed 9-10am, ECEB 3034 Yicheng: Fri 2:30-3:30pm, ECEB 4034 Dimitris: TR 9-9:30am, ECEB 3017
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 Yixuan.
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 | Reading: Lecture 1 by Prof. Srikant, Section 1.1 by Prof. Hajek |
Week 2 | Conditional Probability and Independence, Random Variables, Measurability and Lebesgue Integration | Reading: Lectures 2,3 by Prof. Srikant, Sections 1.2, 1.3, 1.5 by Prof. Hajek |
Week 3 | Basic Inequalities (Markov, Reverse Markov and Chebyshev), Fundamental Functions (Characteristic, Moment Generating and Probability Generating), Important Distributions (Part 1) | Reading: Lectures 3,4 by Prof. Srikant, Sections 1.5, 1.6 by Prof. Hajek |
Week 4 | Important Distributions (Part 2), Jointly Distributed Random Variables, Functions of Random Variables, Jensen's Inequality (Part 1) | Reading: Lectures 4-7 by Prof. Srikant, Sections 1.6, 1.8-1.11, 2.4 by Prof. Hajek |
Week 5 | Jensen's Inequality (Part 2), Gaussian Tail and Chernoff Bounds, CLT, Hoeffding Bound (Part 1) | Reading: Lectures 7-9 by Prof. Srikant, Sections 2.3-2.5 by Prof. Hajek |
Week 6 | Hoeffding Bound (Part 2), Change of Measure, Convergence of Sequences of Random Variables (Part 1) | Reading: Lecture 11 by Prof. Srikant, Sections 2.1 by Prof. Hajek |
Week 7 | Convergence of Sequences of Random Variables (Part 2), Cauchy Criteria, Skorokhod's Representation Theorem, LLN (ms and WLLN), Borel-Cantelli Lemma ('The First Borell – Carntelli Lemma'), Monotone Covnergence Theorem | Reading: Lecture 10 by Prof. Srikant, Sections 1.2, 2.2 by Prof. Hajek |
Week 8 | SLLN, MMSE and LMMSE Estimation | Reading: Lecture 12 by Prof. Srikant, Sections 3.1-3.3 by Prof. Hajek |
Week 9 | Jointly Gaussian Random Variables | Reading: Lecture 13 by Prof. Srikant, Section 3.4 by Prof. Hajek |
Week 10 | DTMCs | Reading: Lecture 14 by Prof. Srikant, Sections 6.1-6.2 by Prof. Hajek |
Week 11 | Martingales, Poisson Process | Reading: Lectures 17-18 by Prof. Srikant, Sections 4.3, 4.5 by Prof. Hajek |
Week 12 | Brownian Motion, Stationarity, Ergodicity, WSS, PSD | Reading: Lectures 18,20,21,23,24,25 by Prof. Srikant, Sections 4.4, 4.6, 4.7, 7.4, 8.1-8.3 by Prof. Hajek |
Weeks 13-14 | Wiener and Kalman Filtering, Random Walks, Azuma-Hoeffding and McDiarmid's Inequalities. Also, Elements of Measure Theory (if time allows) | Reading: Lectures 17, 22, 26 by Prof. Srikant, Sections 3.5, 3.6, 9.1, 9.5, 10.3 by Prof. Hajek |
Midterm 1 | Nov 3 | in class | |
Midterm 2 | Dec 1 | in class | |
Final | Dec 9, 1:30-4:30pm | 3101 Sidney Lu Mech Engr Bldg |