Probability theory I, fall 2015

The [toc] macro is a standalone macro and it cannot be used inline. Click on this message for details.
This macro generates standalone content. As a consequence you need to make sure to use a syntax that separates your macro from the content before and after it so that it's on a line by itself. For example in XWiki Syntax 2.0+ this means having 2 newline characters (a.k.a line breaks) separating your macro from the content before and after it.

News

Teaching schedule

Weeks 36-43, Tuesday12-14 and Thursday 10-12 in room B120.

Exams:

 The course is passed by writing a final exam. Attendance at lectures and

exercise classes is not compulsory (but recommended). Active participation to the exercise class

will raise your grade.   The next  exam is  on thursday 7.4.2016  (yleistentti).

It is possible to take this exam several times without limitations, you are always welcome to improve your grades.

Course material: lecture notes,  English version (last updated on 26.11.2015), Finnish version

Old probability theory course web pages with solved exercises: kevät 2009 syksy 2009, syksy 2012, syksy 2013,   kevät 2015

 Old exam papers

exam problems and solutions, 29.10.2015, suomenkielinen versio.

exam problems and solutions, 4.11.2015, suomenkielinen versio.

The exam program consists of the first 6 chapters of the English version of the lecture notes,

 up to the chapter 6 on stochastic convergence (included),

Literature:

One of these books

J.Jacod- P.Protter: Probability Essentials.

D. Williams: Probability with Martingales.

L. Koralov, Y. Sinai: Theory of Probability and Random Processes, Springer 2007.

Also recommended

O. Kallenberg: Foundations of Modern Probability.

P Malliavin, H Airault, L Kay, G Letac: Integration and Probability

A.N. Shiryaev: Probability  Springer.

A.N. Shiryaev: Problems in Probability, Springer 2012

Registration

 
Did you forget to register? What to do?

Exercises

Assignments

• exercise_sheet_1  , Finnish version,    (9.9.2015)  solutions
• exercise sheet 2    , Finnish version,  (16.9.2015) solutions
• exercise sheet 3 (23.9.2015)solutions
• exercise sheet 4  (30.9.2015) solutions
• exercise sheet 5 (7.10.2015) solutions
• exercise sheet 6 (14.10.2015) solutions
• exercise sheet 7 (28.10.2015) solutions
  
  
• solutions to all exercises written by Petri Tuisku

Exercise classes

Course feedback

Course feedback can be given at any point during the course. Click here.