# 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/Digital Link: Wrapup of Networks and Intro to Channel Capacity Section 7.1-7.5
Information Theory
Lab 6
10/22 Digital Link: Hypothesis Testing, ROC Curves Section 7.6, Section 8.1-8.2
Hypothesis Testing
HW 9
10/27 Digital Link: Statistics, Jointly Gaussian RVs Section 8.3-8.4 Lab 7
10/29 Tracking: Linear Estimation and Regression Section 9.1-9.5
Hilbert Space of RVs
HW 10
11/03 Tracking: Minimum Mean Squared Error Estimation Section 9.6-9.8
11/05 Tracking: Introduction to Kalman Filtering Section 10.1-10.2
Kalman Filter
HW 11
11/10 No Lecture (Midterm 2)   Lab 8
11/12 Tracking: Kalman Filtering Section 10.2-10.4 HW 12
11/17 Route Planning: Markov Decision Problems Section 13 Lab 9
11/19 Route Planning: Linear Quadratic Gaussian Control Section 14 HW 13
11/24 Speech Recognition: Hidden Markov Models, EM Algorithm Section 11
Hidden Markov Models
Lab 10
11/26 No Lecture (Thanksgiving)
12/01 Speech Recognition: Optimization, Stochastic Gradient Descent Section 12 HW 14
12/03 Review