SYLLABUS
PROBABILITY WITH ENGINEERING APPLICATIONS LAB
Spring 2018
Labs are on Thursdays. The deadline for handing in each lab is 11:59pm the first Wednesday after the lab (or if that Wednesday is during semester break, then a week later). The quiz for each lab is at the beginning of the next lab period, except there is no quiz for the last lab. The quiz score for the last lab will be taken to be identical to the lab score. The lowest quiz score and the lowest lab score for each student will not be counted. Quizzes will count for 20% of total course score.Lab # Lab date |
Topics and suggested reading for preparation |
---|---|
Lab 1 1/18 |
Introduction to Python and discrete random variables. See video on probability mass functions: [pmfmean] |
Lab 2 1/25 |
Plotting histograms, exploring law of large numbers, simulating games
Example 1.4.3 in the ECE 313 notes and related videos: PokerIntro, PokerFH2P] Also Problem 1.10 with solutions in back. |
Lab 3 2/1 |
Bernoulli processes, Poisson distribution. Section 2.6 on Bernoulli processes, [SAQ 2.6]; Section 2.7 on Poisson distribution, [SAQ 2.7] |
Lab 4 2/8 |
Standardized random variables, parameter estimation, confidence intervals. 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 2/15 |
Bloom filter/hashing, min hashing. For a description of min hashing see: [SimdocIntro] [Simdoc-Minhash1] queries.pkl |
Lab 6 2/22 |
Random processes and variations of a random walk.
No reading in advance is needed for this lab. |
Lab 7 3/1 |
Introduction to Markov chains and random graphs. 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 3/8 |
Applications of Markov chains: page rank, inference, and cache replacement policies. 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 3/15 |
Binary hypothesis testing, sequential hypothesis testing, and gambler’s ruin. 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 3/29 |
Central limit theorem, change detection, multidimensional
Gaussian distribution. 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 4/5 |
ODEs, failure rates, and evolutionary games. 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 4/12 |
Epidemics, or the spread of viruses. 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. Massoulié, "Thresholds for virus spread on networks," Ann. Appl. Probab. 18:2 (2008), pp. 359-378. |
Lab 13 4/19 |
Linear regression. 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 4/26 |
Principal component analysis, and clustering. 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. |