As noted, the first posts of probability problems have been taken from the homeworks assigned in the Stanford course CE203: "Statistical Models in Civil Engineering." A course syllabus is available here. This course is typically taken by first-year graduate students, although undergraduates can (and do) take the course as well. No prior background in probability or statistics is assumed, although in practice most of the entering graduate students have taken such a course.
These homeworks were developed over a number of years, and were assigned in the precise sequence shown in the archive of all CE203 homeworks. This had a number of intended consequences. For example, the first homework gives students an early appreciation of how probability models are related to (and calibrated from) actual data. It emphasizes practical issues of body-vs-tail fitting, incomplete information, etc. It is shown here how students can quickly grasp the fundamentals of these concepts, before formal statistical concepts are introduced.
The sequence of homework problems was also carefully designed. For example, many students are led to ask why the model of strong and weak hurricanes (Problem 3.3) behaves differently than the apparently similar model of cars and trucks in the prior homework (Problem 2.3). In the questions regarding Poisson models, I can recognize some of the more devious efforts of both the TAs and myself. This is a topic that can easily produce counterintuitive results, and we were not reluctant to capitalize on these.
Finally, as noted on the Problems webpage, this collection is a work in progress. It will seek to include additional problems and solutions, creating an open repository that is intended to aid all who teach these topics. While this may not be the simplest material to teach, I have found it can provide a rewarding experience to both teacher and student. These problems are intended to enrich that experience. Enjoy....
Steve Winterstein (SteveWinterstein@alum.mit.edu)
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