In addition to the regular homework, each student will be required to do a (minor) course project this semester.
For your project topic, you should pick out an interesting theorem/result/example, or an interesting non-trivial (and non-assigned!) problem, related to the class material (e.g. from Sections 8 - 9 or 25 - 35 of the Billingsley textbook, or from some other source). If you have trouble picking a good topic, then you may talk to me about it. Once you have chosen your item you should let me know.
You will then be required to write a short paper (just a few pages) about this topic. Note that it is important to explain your topic in a way that makes it interesting and clear. It is not necessary to cover every last mathematical detail; it is more important to explain the overall point, and to communicate why your topic is interesting.
It may be possible for some students to do an oral presentation instead of a written project; if you would prefer this then please speak to me.
Also, it may be possible for some students to do their project in a group of two or three students, instead of individually. However, all such arrangements must be discussed with me well in advance, and will require a longer and more substantial project. If this interests you, then please speak to me.
To repeat, this is a minor project which should not be more than a few pages long, and should not require a huge amount of research. Rather, it is simply an opportunity for you to explain some interesting aspect of probability theory in your own way.
The project is due by Friday, April 3, 4:00 p.m., and should be put in my mailbox (in Sid Smith 6021) or stuck under my office door (Sid Smith 6024) by that time. Of course, you are welcome to do the project earlier, and hand it in any time before April 3.