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Here is solution to Problem 3 of Test Exam.
Unfortunately there was a typing error in the last point of the text exam. The constant b in the formula for the hazard rate was misplaced. A corrected version of the test exam is now available here. We apologize for this.
It is Christian Agrell! You can contact him on christian.agrell@dnvgl.no if you have questions or concerns about the course which you do not wish to discuss directly with Arne or Kristina.
... in the notes on Risk measures and duality. The corrections have only been made in the final section (Section 4), so it is sufficient to reprint this part. A few additional comments have also been added. The notes can be found here.
For those new to measure theory and convex analysis, yesterday's lecture on convex risk measures may have been a bit much. A good additional reference on measure- and integration theory is Shilling: "Measures, Integrals and Martingales" (you can find it online by google'ing). A good reference on convexity theory is Rockafellar: "Convex Analysis". Both of these books are excellent, but extensive. Only what is in the notes is curriculum for the exam.
My handwritten notes can be downloaded here. They contain some additional comments and explanations. We'll continue next time with the numerical example on buffered environmental contours, before moving on to convex risk measures and duality theory.
Curriculum and a suggested reading list for the Repairable Systems part is given here.
I have today posted new items under the September 12 lecture (exercises, solutions). Bo.
We will have a written final examination. For more details see "Examination: Time and place".
Notes for next week's lecture on buffered environmental contours are available under Syllabus/achievement requirements.
Notes on convex risk measures and duality are available in the same place. This material will be lectured in two weeks from now.
The theory of counting processes appropriate for reliability analysis is given in the book chapter to be downloaded here. Note in particular the treatment of Poisson processes.
The first STK4400 lecture of the semester is August 22. from 9.15-12.00 in room 819, NHA building. The lecture plan for the first few weeks has been posted under Timeplan. It will be updated regularly throughout the semester.
Information about the curriculum with corresponding pdf`s for download can be found there. All of the curriculum will also be posted under Pensum/L?ringskrav throughout the semester.
If you have any questions, please contact either one of us.
See you soon!
Bo (bo.lindqvist@ntnu.no)
Kristina (kristrd@math.uio.no, room 1008, NHA building)
Arne (arne@math.uio.no, room 1006, NHA building)