NMAK11003U Advanced Probability Theory 1 (VidSand1)
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economy
- Sequences of random variables, almost sure convergence, Kolmogorov's 0-1 law.
- The strong law of large numbers.
- Weak convergence of probability measures. Characteristic functions.
- The central limit theorem. Triangular arrays and Lindebergs condition. The multivariate central limit theorem.
- The ergodic theorem.
- Fundamental convergence concepts and results in probability theory.
Skills: Ability to
- use the results obtained in the course to verify almost sure convergence or convergence in law of a sequence of random variables.
- verify conditions for the central limit theorem to hold.
- translate between sequences of random variables and iterative compositions of maps.
Competences: Ability to
- formulate and prove probabilistic results on limits of an infinite sequence of random variables.
- discuss the differences between the convergence concepts.
- 7,5 ECTS
- Type of assessment
- Written examination, 3 hours under invigilationThe course has been selected for ITX exam at Peter Bangs Vej.
- Exam registration requirements
Approval of two assignments during the course is required to register for the exam.
- All aids allowed
NB: If the exam is held at the ITX, the ITX will provide you a computer. Private computer, tablet or mobile phone CANNOT be brought along to the exam. Books and notes should be brought on paper or saved on a USB key.
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
Same as ordinary exam.
If the compulsory assignments were not approved before the ordinary exam they must be resubmitted at the latest two weeks before the beginning of the re-exam week. They must be approved before the re-exam.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
- Theory exercises