Probability theory [MA2409]
News
- exam: August 8, 2012, 15:00 - 16:30 in MW 2001
- post-exam review: August 13, 2012, 11:00 - 12:30 in MI 03.10.011
- second exam: September 26, 2012, 8:00 - 09:30 in Interims-Hörsaal 1 (new room!)
- post-exam review: October 4, 09:30 -10:30 in MI 03.12.020 (Glaskasten)
Lecture
- Lecturer: Prof. Dr. Silke Rolles
- Time and location of the lecture:
Tuesday 8:15 – 9:45 MW 1801 Friday 8:15 – 9:45 MI HS 1 - Prerequisites: Maß- und Integrationstheorie (MA 2003) and Einführung in die Wahrscheinlichkeitstheorie (MA 1401)
- Literature: The books will be on reserve in the library (Semesterapparat).
- Measure theory:
- M. Brokate, G. Kersting: Maß und Integral, Birkhäuser, 2010. Link to the ebook
- The appendix of R. Durrett: Probability: theory and examples, fourth edition, Cambridge University press, 2010.
- Probability theory:
- P. Billingsley: Probability and measure, third edition, Wiley, 1995.
- K.L. Chung: A course in probability theory, third edition, Academic Press, 2001.
- R. Durrett: Probability: theory and examples, fourth edition, Cambridge University press, 2010.
- A. Klenke: Wahrscheinlichkeitstheorie, 2. Auflage, Springer, 2008. Link to the ebook of the first edition
- A. Klenke: Probability theory, Springer, 2008.
- D. Williams: Probability with martingales, Cambridge University Press, 2005.
- Measure theory:
- Syllabus
- Lecture notes will be posted in TUM-Online approximately one week after the lecture.
Final exams
- August 8, 2012, 15:00 - 16:30 in MW 2001
- September 26, 2012, 8:00 - 09:30 in Interims-Hörsaal 2
- Remark on the exam: calculators, lecture notes, etc. are not allowed
Homework and Tutorials
- Homework will be assigned every week. Every Tuesday a problem sheet will be handed out during the lecture. You should try to solve all homework problems. You can work in groups of up to 3 students. Your solutions can be written in German or in English. Please put your solutions in the mailbox "probability theory" in the basement of the mathematics building. Your homework is due on Tuesday at 12:00 one week after it was assigned.
- Graded homework will be returned during the tutorials one week after it was handed in. Homework which is not picked up during the tutorials can be found in the shelf located on the right-hand side after the first glass door in building part 03.12.
- Grades on homework: Each exercise is graded from 0 to 4 points, where 4 stands for a perfect solution, 3 for few minor mistakes or missing arguments, 2 for major lacks and 1 for reasonably worked on. If an exercise consists of several parts, each of them has to be worked out reasonably for the whole exercise to count as reasonably worked out.
- Final grade: The final grade is the grade obtained in the final exam plus a possible bonus. If 80% of all homework problems are reasonably worked out, then you get a bonus: If you pass one of the final exams (i.e. your grade is 4.0 or better), then your grade is improved by 0.3 (for example 4.0 becomes 3.7, 3.7 becomes 3.3, 3.3 becomes 3.0 etc.). A grade of 1.0 is not changed.
- Time and location of the tutorials:
Group time location tutor 1 Thursday, 08:00 - 10:00 MI 03.06.011 Thomas Kochler 2 Thursday, 12:00 - 14:00 MI 02.04.011 Thomas kochler 3 Friday, 10:00 - 11:30 MI 02.04.011 Julia Wagner 4 Friday, 10:00 - 12:00 MW 0337 MI 02.08.020Johannes Keller 5 Friday, 10:00 - 12:00 MI 02.10.011 Mathias Rafler 6 Friday, 12:00 - 14:00 MI 03.08.011 Mathias Rafler
- Teaching assistants: Johannes Keller, Renate Klaffki, Thomas Kochler, Mathias Rafler, Franz, Rembart, Julia Wagner
Repetition
- Monday, May 21, 16:15 - 17:45, MW 0001: types of convergence of random variables and relations, Borel-Cantelli lemma, tail-sigma-algebra and Kolmogorv's 0-1-law, product spaces and independence
- Monday, June 25, 16:15 - 17:45, MW 0001: weak convergence, characteristic functions, Levy's continuity theorem and central limit theorems
- Monday, July 16, 16:15 - 17:45, IHS 2: conditional expectation, martingales, martingale convergence theorems, martingale inequalities
Homework problems
Problem sheet | Topic | Due date | Comments |
---|---|---|---|
Sheet 1 | probability measures and measurability | April 24 | |
Sheet 2 | inequalities | May 2 | |
Sheet 3 | independence infinte products | May 8 | |
Sheet 4 | independence and convergence | May 15 | T4.1: X_n independent |
Sheet 5 | convergence and sums | May 22 | |
Sheet 6 | 0-1 law, SLLN, weak convergence | May 30 | see additions to 6.3 |
Sheet 7 | weak convergence, a central limit theorem | June 5 | 7.2(b): Asymptotik ist k_n/sqrt{n/2} |
Sheet 8 | characteristic functions | June 12 | |
Sheet 9 | characteristic functions and central limit theorem | June 19 | lambda_i is a version of a_i |
Sheet 10 | conditional expectation | June 26 | u in T10.1 added |
Sheet 11 | conditional expectation, martingales | July 3 | 11.3(b): Y_n identically distributed |
Sheet 12 | martingale application | July 10 | |
Sheet 13 | martingale application | July 17 |