NMAK11003U Advanced Probability Theory 1 (VidSand1)
Volume 2016/2017
Education
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economy
Content
- 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.
Learning Outcome
Knowledge:
- 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.
Recommended Academic Qualifications
Mål- og integralteori
(MI)
Teaching and learning methods
5 hours of lectures and 3
hours of exercises per week for 7 weeks.
Workload
- Category
- Hours
- Exam
- 3
- Lectures
- 35
- Preparation
- 147
- Theory exercises
- 21
- Total
- 206
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Exam
- Credit
- 7,5 ECTS
- Type of assessment
- Written examination, 3 hours under invigilation---
- Aid
- 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
- Re-exam
Same as ordinary exam
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK11003U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- A
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Ernst Hansen (8-69766c6572776972447165786c326f7932686f)
phone 35 32 07 73, office 04.3.12,
Saved on the
09-03-2016