Probability and Random Processes

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

Office Hours: WF 10-11am (v)


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
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