# 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.

## 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.

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, Convergence, Strong Law of Large Numbers 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 Networks: Queuing, Poisson Processes Section 5
Random Graphs
10/12 Networks: Continuous Time Markov Chains Section 6.1-6.2
CTMCS
10/14 Networks: CTMC Uniformization, Stationary Distribution Section 6.3-6.4
10/19 Networks: Product-Form Networks
10/21 Networks: Wrap-up
10/26 Digital Link: Introduction to Entropy Section 7.1-7.5
Information Theory
10/28 Digital Link: Huffman Codes and BSE Channel Capacity Section 7.1-7.5
Information Theory
11/02 Digital Link: MAP and MLE
11/04 No Lecture (Midterm 2)
11/09 Digital Link: Hypothesis Testing, ROC, Neyman-Pearson Theorem Section 7.6, Section 8.1-8.2
Hypothesis Testing
11/11 No Lecture (Veteran’s Day)
11/16 Digital Link: Jointly Gaussian RVs Section 8.3-8.4
11/18 Tracking: LLSE Section 9.1-9.5
Hilbert space of RVs
11/23 Tracking: MMSE Section 9.6-9.8
11/25 No Lecture (Thanksgiving Break)
11/30 Tracking: Kalman Filtering Section 10.2-10.4
Kalman Filter
12/02 Review