Stochastics III

Dr. Tim Brereton

Teaching assistant
Lisa Handl

Time and Place

Monday, 10 am - noon (N24, H14)

Excercise session
Wednesday, noon - 2 pm (N24, H14)   (every second week)


2 hours lecture and 1 hours excercise
Credit points: 4

Master students have the opportunity to earn 2 extra credit points by attending a reading course (see below).


Probability Calculus ("Elementare Wahrscheinlichkeitsrechnung und Statistik") and Stochastics I.

Intended Audience

Bachelor and Master students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"; students in "Master of Finance".

Note that the reading course is open to Master's students only.


Main topics of the lecture are:

  • multivariate normal distribution
  • linear und general linear models
  • tests for distributional assumptions
  • non-parametric localization tests

Requirements and Exam

In order to participate in the final exam, it is necessary to earn 50% of the points on all problem sheets. Students who want to do so are kindly asked to register for the 'Vorleistung' in the LSF-'Hochschulportal'.

Time and place

First exam:

Thursday, March 5
from 10 am to noon (1 pm incl. reading course) in H22

Second exam:

Friday, April 10
from 10 am to noon (1 pm incl. reading course) in H3

Authorized examination aids

Participants will be allowed to bring a one-sided (!) handwritten A4 sheet if they take the Stochastics III exam, and a one-sided handwritten A5 sheet if they take the reading course exam with useful results from the lectures and exercises to the exam (both if they take both). A non-programmable calculator is permitted as well.

Master students taking the reading course will need to register for two exams: "Stochastik III (Ausgewählte Kapitel der Statistik)" AND "Lesekurs zur Stochastik III".

The first one is the standard Stochastics III exam (4 credit points) and the second one is (only) about the reading course material (2 credit points). These 2 exams are formally independent, there will be separate marks. In particular, each of them can be passed or failed independently.

Please make sure you register for the right 'Vorleistung(en)' depending on the exam(s) you want to take!

The organization of the exams will be as follows.

Everyone should come at 10 am, no matter which exam(s) you take. If you take the Stochastics III and the reading course exam, you will get both exams at the same time. After 2h we will collect the Stochastics III exams and you will have 1 more hour to finish the reading course exam.

This way everyone has the same time for the exams but you still have the possibility to finish early.

The second exams are corrected!

You can find the number of points you obtained in the SLC in the section "Prüfungsleistung", the second Stochastics III exam is number 3 and the second reading course exam is number 4. The associated marks are indicated in the following tables:

Stochastics III
1,045 - 50
1,343 - 44,5
1,740 - 42,5
2,037 - 39,5
2,334 - 36,5
2,732 - 33,5
3,030 - 31,5
3,328 - 29,5
3,726,5 - 27,5
4,025 - 26
5,00 - 24,5
Reading Course
1,021,5 - 25
1,320 - 21
1,718,5 - 19,5
2,017 - 18
2,315,5 - 16,5
2,714 - 15
3,013 - 13,5
3,312 - 12,5
3,711 - 11,5
4,010 - 10,5
5,00 - 9,5

The post-exam review for the second exams will take place on Friday, April 17 from 1:30 to 2:30 pm in Lisa Handl's office (room 1.42 in Helmholtzstr. 18).

Reading Course

Master's students taking the reading course will be required to be familiar with the section “Goodness-of-Fit Tests” in Volker Schmidt's lecture notes. This section will be part of the reading course exam though it will not be covered in class.

Here are some exercises to help you understand and practice the material you read:

Extra Problem Sheet      Files:  rats.txt   steel.txt

If you want to practice some more, you can work through Examples 5.4.1 and 5.4.2 in the lecture notes. These are very nice worked out examples clarifying the material.

Problem Sheets

Problem Sheet 01     R code 01

Problem Sheet 02     R code 02

Problem Sheet 03     R code 03     Files:  murders.txt   production.txt

Problem Sheet 04     R code 04     Files:  velocity.txt   ski.txt   water.txt

Problem Sheet 05     R code 05

Problem Sheet 06     R code 06     Files:  cars.txt

Problem Sheet 07     R code 07     Files:  medicine.txt

In order to receive points for your problem sheets, a registration at SLC is required.

Here are links to several introductions to the programming language R, which is needed for some of the exercises:

A (very) short introduction:   in English      in German  
A long introduction:   in English      in German  

Lecture Notes

The lecture will be based on the lecture notes of Prof. Dr. Volker Schmidt:

Lecture Notes (English)        Lecture Notes (German)


  • Büning, H., Trenkler, G. (1994)
    Nichtparametrische statistische Methoden
    de Gruyter, Berlin

  • Cressie, N.A. (1993)
    Statistics for Spatial Data
    J. Wiley & Sons, New York

  • Dobson, A.J. (2002)
    An Introduction to Generalized Linear Models
    Chapmen & Hall, Boca Raton

  • Hastie, T., Tibshirani, R., Friedman, J. (2001)
    The Elements of Statistical Learning
    Springer, New York

  • Koch, K.R. (1997)
    Parameterschätzung und Hypothesentests in linearen Modellen
    Dümmlers-Verlag, Bonn

  • Kroese, D.P., Chan, J.C.C. (2014)
    Statistical Modeling and Computation
    Springer, New York

  • Lehmann, E.L. (1999)
    Elements of Large-Sample Theory
    Springer, New York

  • Lehmann, E.L., Romano, E.J. (2005)
    Testing Statistical Hypotheses
    Springer-Verlag, New York

  • Vapnik, V.N. (1998)
    Statistical Learning Theory
    J. Wiley & Sons, New York



Teaching assistant

Mailing List

We installed a mailing list to keep you up-to-date with important or short-term information regarding the course. You can subscribe on or by sending this email.

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The second exams are corrected!

The auxiliary means you may use during the exam have been updated (see exam section).

Please bring a (non-programmable) calculator to the exam!

The last problem sheet has been marked. If you like, you can pick it up in Lisa Handl's office.

The reading course section has been updated.

The exam dates and times are online now. Please not that the rooms have been changed.

The lecture notes are available as printouts now (in English), you can pick them up in Dr. Brereton's office (room 1.43, Heho 18).

Anonymous Feedback

On this page you can send us anonymous comments on the lectures and exercise lessons.