# Probability and Random Processes

Fall 2020
Shyam Parekh
TuTh 11-12:30 PM, Internet/Online

Office Hours: Friday 1-2pm

## Announcements

• Welcome to EECS 126! Please read the course info, join Piazza, and join Gradescope (code 9P4JYV).

## Lecture Schedule

Readings refer to Walrand’s “Probability in Electrical Engineering and Computer Science”. Online notes only serve as optional supplemental readings, and will not directly correspond to the lectures or textbook (see content).

Schedule is subject to some changes.

08/27 Elementary Probability: Symmetry, Expectation, Conditioning Appendix A.1-A.5 HW 1
09/01 Elementary Probability: Bounds, Law of Large Numbers Appendix A.6-A.9 Lab 0
09/03 Basic Probability: Bayes Rule, Conditional RVs Appendix B.1-B.3 HW 2
09/08 Basic Probability: Discrete RVs, Joint RVs, Independence Appendix B.4-B.5 Lab 1
09/10 Basic Probability: Continuous RVs, Orthogonality Appendix B.6-B.7 HW 3
09/15 PageRank: Discrete Time Markov Chains Section 1
Markov Chains
Lab 2
09/17 PageRank: Reversibility, Infinite States, Classification Section 2.1-2.3
Reversibility
HW 4
09/22 PageRank: Big Theorem Section 2.4-2.5
Convergence

09/24 No Lecture (Midterm 1)   HW 5
09/29 Multiplexing: Gaussian RVs, CLT, Confidence Intervals Section 3 Lab 3
10/01 Multiplexing: Central Limit Theorem, Applications of Characteristic Functions Section 4 HW 6
10/06 Multiplexing/Networks: Wrapup of Multiplexing and Intro to Networks Section 4 and Section 5.1-5.5
Random Graphs
Lab 4
10/08 Networks: Queueing, Poisson Processes Section 5.6-5.10 HW 7
10/13 Networks: Continuous Time Markov Chains Section 6.1-6.2
CTMCS
Lab 5
10/15 Networks: CTMC Uniformization, Stationary Distribution Section 6.3-6.4 HW 8
10/20 Networks: Product-Form Networks   Lab 6
10/22 Networks: Wrapup   HW 9
10/27 Digital Link: MAP & MLE   Lab 7
10/29 Digital Link: Huffman Codes & BSE Channel Capacity Section 7.1-7.5
Information Theory
HW 10
11/03 Digital Link: Hypothesis Testing, ROC, Neyman-Pearson Theorem Section 7.6, Section 8.1-8.2
Hypothesis Testing
Lab 8
11/05 Digital Link: Jointly Gaussian RVs Section 8.3-8.4 HW 11
11/10 No Lecture (Midterm 2)
11/12 Tracking: LLSE Section 9.1-9.5
Hilbert Space of RVs
HW 12
11/17 Tracking: MMSE Section 9.6-9.8
11/19 Tracking: Kalman Filtering Section 10.2-10.4
Kalman Filter
HW 13
11/24 Route Planning: Introduction Section 13 Lab 9
11/26 No Lecture (Thanksgiving)
12/01 Speech Recognition: Introduction Section 11
Hidden Markov Models
HW 14
12/03 Review   Lab 10