ECE 314 Syllabus Fall 2021 (Tentative)

TENTATIVE SYLLABUS

PROBABILITY IN ENGINEERING LAB

Fall 2024

Lab Due Date Topics and Suggested Reading for Preparation
Lab 1
Tues. 9/3 10pm 		Introduction to Python and discrete random variables. (Video )
See video on probability mass functions: [pmfmean]
Lab 2
Tues. 9/10 10pm 		Plotting histograms, exploring law of large numbers, simulating games (Video)
Example 1.4.3 in the ECE 313 notes and related videos: [PokerIntro, PokerFH2P] Also Problem 1.10 with solutions in back.
Lab 3
Tues. 9/17 10pm 		Bernoulli processes, Poisson distribution. (Video)
Section 2.6 on Bernoulli processes, [SAQ 2.6]
Section 2.7 on Poisson distribution, [SAQ 2.7]
Lab 4
Tues. 9/24 10pm 		Standardized random variables, parameter estimation, confidence intervals. (Video)
This lab is directly related to the ECE 313 concepts listed, covered in Sections 2.2, 2.8, and 2.9 of the course notes. Two relevant SAQs: [SAQ 2.8] [SAQ 2.9]
Lab 5
Tues. 9/31 10pm 		Bloom filter/hashing, min hashing. (Video)
For a description of min hashing see: [SimdocIntro] [Simdoc-Minhash1]
Lab 6
Tues. 10/8 10pm 		Random processes and variations of a random walk. (Video)
No reading in advance is needed for this lab.
Lab 7
Tues. 10/15 10pm 		Introduction to Markov chains and random graphs. (Video)
If necessary it'd be good for you to review basic linear algebra, especially matrix multiplication. It would be helpful (but not necessary) for you to read a little about Markov chains on Wikipedia.
Lab 8
Tues. 10/22 10pm 		Applications of Markov chains: page rank, inference, and cache replacement policies. (Video)
Builds on previous lab. For background you could read about PageRank and Cache algorithms on Wikipedia. You could also see Problem 2.9 in the course notes about the Zipf distribution.
Lab 9
Tues. 10/29 10pm 		Binary hypothesis testing, sequential hypothesis testing, and gambler's ruin. (Video)
Not much advance preparation is needed, but it would be helpful for you to review (i) Section 2.11.1 on the maximum likelihood decision rule and (ii) Problem 2.18. You might also briefly review Lab 6.
Lab 10
Tues. 11/5 10pm CT 		Central limit theorem, change detection, multidimensional Gaussian distribution. (Video 1)(Video 2)
Change detection is achieved by using the idea of sequential hypothesis testing explored in Lab 9. While not critical, it would be helpful for you to review the central limit theorem in Section 3.6.3 (revisited in Section 4.10) and to read about the joint Gaussian distribution in Section 4.11.
Lab 11
Wed. 11/12 10pm 		ODEs, failure rates, and evolutionary games. (Video)
It would help for you to briefly review failure rate functions in Section 3.9 and the area rule for expectation in Section 3.8.3. This lab gives a brief glimpse of game theory, and how it can be used to model the dynamics of interacting populations of individuals. A nice introduction to this topic is given in Chapter 7 of Easley and Kleinberg Networks, Crowds, and Markets, Reasoning about a Highly Connected World,
Lab 12
Tues. 11/19 10pm 		Epidemics, or the spread of viruses. (Video)
You would probably find it useful to spend ten or twenty minutes before the lab reading about "SIR model" and "spread of diseases" on the Internet. For more information, an advanced but fairly readable analysis is given in M. Draief, A. Ganesh, and L. Massouli, "Thresholds for virus spread on networks," Ann. Appl. Probab. 18:2 (2008), pp. 359-378.
Lab 13
Tues. 12/3 10pm 		Linear regression. (Video 1)(Video 2)
It would be helpful to study up on linear minimum means square error estimators in Section 4.9.3 in preparation of this lab. That covers what is called simple linear regression (estimation of a one-dimensional variable from another). The lab goes into multiple linear regression as well (estimation of a one-dimensional variable from a set of other variables), which is discussed in the ECE 534 notes, Section 3.3.2.
Lab 14
Tues. 12/10 10pm 		Principal component analysis and clustering. (Video 1)(Video 2)
It would be helpful for you were to spend half an hour before the lab reading about principal component analysis (PCA) on Wikipedia or other websites. The eigen decomposition behind PCA is briefly discussed in the ECE 534 notes, Section 3.1.