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Grading is finished and sent. A solution to the exam can be found under "suggested solutions" or by clicking here.
The trial exam will start in room 126 at 14:00 and continue in room 1020 (10th floor) from 16:00 to 18:00.
Remember that no aids or extra material is allowed. Bring something to write with. I will bring the exam printed and some paper.
The trial exam (as well as the exam) will be structuted as follows: four exercises where the first one will be of theoretical nature and the rest applied. The content of the exercises will be:
Problem 1 (Theory): define or outline some concepts, results or theorems.
Problem 2 (Random variables): usual stuff about random variables and convergence.
Problem 3 (Conditional expectation): mainly conditional expectation, but it can also contain things from random variables and convergence.
Problem 4 (Martingales): anything related to martingales and/or stopping times from the last chapter.
Note that Problem 2 and 3 deal with random variables, convergence and conditiona...
The solution to the assigment is now published. Please, check carefully and compare with yours.
You did a good job! The only thing that many did wrong is the step to take the infinite sum outside the integral in Problem 2a, which is actually pushing a limit out of the integral and, therefore, must be justified. Check whether you did this mistake and the solution. The step per se is not wrong, but it must be justified.
The way forward is to continue with Chapter 8 on martingales and stopping times. This is the last chapter. Then we will have a trial exam and I will publish exams from previous years.
Good luck!
I have updated the lecture notes. Things to note:
1) You have some solutions for Chapter 5. Try to solve the exercises from Chapter 5 if you have not done so, before checking the solutions.
2) Now you have everything until Chapter 6 (included). You can start trying to solve the exercises of Chapter 6 (Exercise 6.4 was solved on the blackboard yesterday).
3) I have rewritten the proof of the equivalent definition of almost sure convergence. It is the same as yesterday, but more rigorous and justifying measurability inside the probability. Also, please check the proofs of: Proposition 6.3.1 and Proposition 6.4.1.
4) Next week we will start Chapter 7 on conditional expectation and Wednesday will be devoted to solving more exercises from Chapter 5 and 6.
The mandatory assignment is now available in the menu below. You can also reach it by clicking the word assignment, not this one, but this one: assignment.
Deadline is 17th of October, at 14:30. Delivery of the assignment in canvas: canvas.uio.no in a single pdf file.
Good luck!
PS: I have also uploaded solutions to some exercises until Chapter 5.
All students are welcome to a social event on the 26th of September at 16:00 in the big room on the 12th floor.
Check the event in the link below and register if you would like to attend:
I have uploaded an updated version of the lecture notes with solutions for some exercises.
Thank you for a nice and cooperative discussion today! We will try to find the teaching methodology that maximizes overall utility :) I have been thinking and I have a proposal for the "practical" part of the course which I will present to you tomorrow (28th og Aug.). It is basically the following:
Lectures will be on the blackboard, preferably on Tuesdays. One week before you will be given a list of exercises to solve. On selected Wednesdays, you will solve the exercises and I will walk around and help you during the first hour. You can also come with your proposed solutions and ask me. In this way, I will get an idea of which exercises are most demanding. Those will be solved on the blackboard during the second hour, if needed. Only the solutions to the exercises that we have not been solved in the classroom will be uploaded, thus encouraging students to come a...
The lecture notes are now updated. There is now a lot of material from Chapter 3, but you do not need to look at it yet. Now you can find the exercises from Chapter 3 and you are ready to solve any exercise from 3.1 to 3.12. Solve those that you manage or have time to.
From yerterday's lecture I have added a deeper discussion into the topic of completeness of measures. However, I prefer that you solve the exercises.
The student representatives for this semester are:
Georg Ziegler Helle, georgzh at math.uio.no
Mohit Varma, mohitv at math.uio.no
The date for handing in the assignment is 17th of October at 14:30. The assignment needs to be handed in on Canvas (canvas.uio.no) in a pdf file. It will be published two weeks before the due date.
Dear students!
I have uploaded a first version of the lecture notes. You will find them in the menu below on the course webpage or by clicking here. There you will find:
- A gentle introduction on "what probability is or can be".
- Some useful preliminary material.
- The start of the syllabus: measure theory.
The first two chapters are not compulsory, but it may be nice to take a look. You can take a look while you are in the public transport or on a plane or train coming back from holidays, or simply at home during a rainy evening. It is meant as a soft reading. However, it is important that you understand the content of Chapter 2 reasonably well. You can also try Exercise 2.1, 2.2 and 2.3 if you wish.
Obs: Lecture notes will be updated weekly. Syllabus starts from Chapter 3. Exercises will come and solutions as well. Please, come to the lectures for better understan...
Time and place:?Our?first lecture will take place on Tuesday 20th of August at 10:15 am?in the lecture room 126 in Niels Henrik Abels hus?(the same as the Department of Mathematics). See the schedule of the course here.
The language of the course will be chosen during the first lecture. The language of the written notes and exercises will be?English.?In any case, you may hand in your assignment and exam in English or any other Scandinavian language.
Literature/lecture material:?We will use the following supporting book for this course: Jacod J., Protter P.?Probability Essentials, 2nd Ed. 2004. Springer Berlin Heidelberg.
However, I will work out my own lecture notes progressively, which I will update every week with new content and exercises. There you will find all the material you need. You may use the book as supporting m...