Module 24-M-Prob1 Probability Theory for Quantitative Economics

Faculty

Person responsible for module

Regular cycle (beginning)

Every winter semester

Credit points and duration

7 Credit points

For information on the duration of the modul, refer to the courses of study in which the module is used.

Competencies

Non-official translation of the module descriptions. Only the German version is legally binding.

This module introduces the students to the fundamentals of rigorous probability theory.
The students learn, how to establish stochastic models to solve problems in situations affected by random influences. They are able to analyze these models with probabilistic standard techniques. These mathematical competences allows them to deduce consequences, which are relevant for the solution of the considered problems. In addition, this lecture prepares the students to go on to advanced probability-related topics such as Brownian motion and Ito calculus.

Content of teaching

This module consists of one lecture with following content:

  • Introduction in elementary set theory and combinatorics
  • Axioms of probability theory
  • conditional probability and independence
  • discrete random variables and distributions (with standard examples), expectation and variance
  • continuous random variables (with standard examples)
  • limit theorems: weak convergence of random variables and characteristic functions, law of large numbers, central limit theorem

This lecture prepares the student to go on to advanced probability-related topics such as Brownian motion and Ito calculus.

Books: JACOD, J. and PROTTER, P., Probability Essentials, Springer, second printing 2004. [Chapters 1-21]

Recommended previous knowledge

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Necessary requirements

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Explanation regarding the elements of the module

Module structure: 1 SL, 1 bPr 1

Courses

Probability Theory
Type lecture
Regular cycle WiSe
Workload5 90 h (60 + 30)
LP 3 [Pr]
Excercise on Probability Theory
Type exercise
Regular cycle WiSe
Workload5 60 h (30 + 30)
LP 2 [SL]

Study requirements

Allocated examiner Workload LP2
Teaching staff of the course Excercise on Probability Theory (exercise)

Regular completion of exercises with a recognisable solution approach. Participation in exercise groups (presentation of calculation exercises twice when asked. The organiser may replace some of the exercises by exercises in attendance).

 see above see above

Examinations

written examination o. oral examination
Allocated examiner Teaching staff of the course Probability Theory (lecture)
Weighting 1
Workload 60h
LP2 2

Written examination of usually 90 minutes or oral examination of usually 20-30 minutes.

The module is used in these degree programmes:

Degree programme Profile Recom­mended start 3 Duration Manda­tory option 4
Quantitative Economics / Master of Science [FsB vom 15.02.2013 mit Änderungen vom 01.07.2015 und 31.03.2023] 1. one semester Obli­gation
Quantitative Economics / Master of Science [FsB vom 15.02.2013 mit Änderungen vom 01.07.2015 und 31.03.2023] International Track 1. one semester Obli­gation

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Legend

1
The module structure displays the required number of study requirements and examinations.
2
LP is the short form for credit points.
3
The figures in this column are the specialist semesters in which it is recommended to start the module. Depending on the individual study schedule, entirely different courses of study are possible and advisable.
4
Explanations on mandatory option: "Obligation" means: This module is mandatory for the course of the studies; "Optional obligation" means: This module belongs to a number of modules available for selection under certain circumstances. This is more precisely regulated by the "Subject-related regulations" (see navigation).
5
Workload (contact time + self-study)
SoSe
Summer semester
WiSe
Winter semester
SL
study requirement
Pr
Examination
bPr
Number of examinations with grades
uPr
Number of examinations without grades
This academic achievement can be reported and recognised.

Sidebar

Elements of the module

Courses

Study requirements

Examinations

Programme of lectures (eKVV)

Programme of lectures (eKVV)

Show lists of modules

Quantitative Economics / Master of Science

Quantitative Economics / Master of Science // International Track