Probability and Random Processes

Fall 2021
Shyam Parekh
TuTh 5-6:30 PM, 2060 VLSB

Office Hours: WF 10-11am (v)

Announcements

Welcome to EECS 126! Please read the course info, join Piazza, and join Gradescope (code 74PB3B).
Please note this is an in-person class with no recorded lectures or discussions, and in-person exams. There will, however, be a few virtual office hours and discussions. See calendar for the schedule.
Here’s an anonymous feedback form for you to provide any suggestions to help us improve the class.
For office hours queue, use this Google Sheets link.

Lecture Schedule

Readings refer to Walrand’s Probability in Electrical Engineering and Computer Science. Additionally, these Jupyter Notebooks provide extra reinforcement for the textbook. Online notes will serve as optional supplemental readings, and will not directly correspond to the lectures or textbook (see content). The B&T textbook may also be useful, but is not the primary textbook.

Schedule is subject to some changes.

Date	Topics	Readings
08/26	Elementary Probability: Symmetry, Expectation, Conditioning	Appendix A.1-A.5
08/31	Elementary Probability: Bounds, Law of Large Numbers	Appendix A.6-A.9
09/02	Basic Probability: Probability Space, RVs, Borel-Cantelli	Appendix B.1
09/07	Basic Probability: Bayes Rule, Conditional RVs	Appendix B.2-B.3
09/09	Basic Probability: Discrete RVs, Joint RVs, Independence	Appendix B.4-B.5
09/14	Basic Probability: Continuous RVs, PageRank: Discrete Time Markov Chains, Big Theorem	Appendix B.6-B.7 Section 1.1-1.3 Markov Chains
09/16	PageRank: Big Theorem	Section 1.3-1.4, 2.5
09/21	PageRank: Big Theorem, Hitting Time	Section 1.5, 2.1-2.4
09/23	No Lecture (Midterm 1)
09/28	PageRank: Convergence, SLLN; Multiplexing: Gaussian RVs	Convergence Section 3
09/30	Multiplexing: Central Limit Theorem, Confidence Intervals	Section 3
10/05	Multiplexing: Characteristic Functions	Section 4
10/07	Infinite DTMC, Poisson Processes	Section 5, 15
10/12	Poisson Processes, CTMC	Section 6.1-6.2 CTMCS
10/14	CTMC	Section 6.3-6.4
10/19	CTMC, Uniformization and Queues
10/21	Queues
10/26	Jackson Networks and Random Incidence Paradox	Section 7.1-7.5 Information Theory
10/28	Digital Link: MAP and MLE
11/02	Digital Link: Entropy, Huffman Codes
11/04	No Lecture (Midterm 2)
11/09	Digital Link: BSC Channel Capacity	Section 7.6, Section 8.1-8.2 Hypothesis Testing
11/11	No Lecture (Veteran’s Day)
11/16	Digital Link: Hypothesis Testing, ROC, Neyman-Pearson Theorem	Section 8.3-8.4
11/18	Digital Link: Jointly Gaussian RVs	Section 9.1-9.5 Hilbert space of RVs
11/23	Tracking: LLSE	Section 9.6-9.8
11/25	No Lecture (Thanksgiving Break)
11/30	Tracking: MMSE	Section 10.2-10.4 Kalman Filter
12/02	Tracking: Kalman Filtering