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Here are the problem set, the solutions, and the grading instructions.
I have corrected the solution to trial exam 1, problem 4a, where the indices were all mixed up. I have also added an extra step to the argument for integrability in trial exam 3, problem 3b.
The exam has 11 problems (1, 2a, 2b, etc) and is quite similar in format to the trial exams (perhaps a bit longer than some of them, so keep an eye on time). All problems count 10 points, and the exam is graded according to the Math department's criteria. The exam is without aids of any kind (not even a simple calculator is allowed, but then I can't imagine what you should have used it for!) The formula sheet will be attached to the exam, and you are not allowed to use your own copy (but keep the misprint mentioned here in mind!). If there is a problem you cannot do, you may still use the result from that problem in later problems (as most questions are of the form "show that...", this is often possible). R...
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https://nettskjema.no/a/mfu2019f-stkmat3710
This is particularly important with a new course such a this!
A misprint has been detected on the formula sheet in the formula for characteristic function of a normal random variable (the last t in the exponent should be t2). The mistake has been corrected in the version that is now on the semester page. Unfortunately, it is too late to correct the mistake on the formula sheets that will be handed out at the exam, but I will remind you of it as go through the room. Also note that I have added two more formulas to the sheet, one on Lebesgue-Stieltjes integrals and one at the very end on convergence to the exponential function (these formulas are on both the web and the exam version).
The solutions to all three trial exams are now available. Look under "Problems".
As there is a lot to remember in this course, I have made a formula sheet with the main definitions and results. This sheet will be distributed at the exam (so you don't have to bring it with you). To keep it short, I have often omitted conditions that should be clear from the context. Please be aware that the results and definitions on the sheet are not the only ones that may be needed at the exam!
The three trial exams are now available. They and the mandatory assignment should give a good impression of what the exam problems will look like. Solutions will follow later.
I have written a short note on stopping times and filtrations which I hope may make these concepts more intuitive.
The lecture today, Thursday October 31, has been moved to room 126 in NHA.
A suggested solution is available here.
I have written a short note to motivate the Fourier Inversion Theorem that is just taken for granted in the textbook.
The physical lecture on Monday, October 7th, is canceled, but will be replaced by a podcast.
There was a misprint in the original version of the mandatory assignment that has now been corrected. The misprint was in the displayed formula in Problem 1, where the names of the indices on the right hand side should have been p and q rather than i and j.
You'll find the mandatory assignment here. The deadly is Thursday, October 17th at 14.30.
I have dropped Problem 3.1 from the list of problems for this Thursday. The reason is that the problem is not well-posed with the background we have: If the definition of the measure nu is to make sense, the integral on the right hand side has to be interpreted as a Lebesgue integral and not as a Riemann integral, and we have not developed Lebesgue integration (if you happen to know Lebesgue integration, the problem is doable).
As we didn't have time for a full solution of this problem in class, I have made a written solution that you can find here.
As the first load of textbooks disappeared before everybody had time to pick up a copy, I have made an electronic version of the relevant parts of Chapter 2.
The recordings replacing the canceled lecture on Monday, September 2, are now available here.
The (physical) lecture on Monday September 2. has to be canceled as I am at Sundvollen for the introductory seminar for the new MAEC students. The plan is to replace the physical lecture by a podcast, but I am not quite sure when I will have the time (and the room!) to make the recording.
Some copies have now arrived, but not the full load. There were four copies left this morning, so run and buy!
I was asked in the first lecture of an example of a nonmeasurable set. This is not straight forward as (luckily!) all naturally occurring sets are measurable. If you want to see the construction of a nonmeasurable set, there is a video explanation here.
As the textbook hasn't arrived at the bookstore yet, I have taken the liberty of scanning the part of Chapter 1 that is on the syllabus. The book (both paper and electronic version) is actually on sale from the publisher's homepage at the moment, but I don't know how long it will take for the printed version to get here.
There is a lot of manipulations with sets in STK-MAT3710, and if this is unfamiliar (or forgotten), you may want to take a look at the first pages of these notes (written for another course years ago).
I have now updated the syllabus and the schedule, but be aware that everything is tentative: As this is the first time the course is given, we may have to adjust a few things as we go along.