Duration
30h Th, 20h Pr
Number of credits
| Bachelor in mathematics | 5 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Short table of contents
- Probability spaces
- Elementary discrete models
- Random variables
- The expectation operator
- Classical probability distributions
- Univariate convergence of rv
Learning outcomes of the learning unit
At the end of the course the student will have a deep understanding of the concepts at the heart of probability theory. He will know the fundamental probability distributions and will be able to competently assess any risk.
Prerequisite knowledge and skills
A good mastery of elementary calculus is indispensable to follow this class.
Planned learning activities and teaching methods
Ex cathedra classes as well as exercise sessions.
Mode of delivery (face-to-face ; distance-learning)
Recommended or required readings
Complete course notes (including exercise sets) will be made available through eCampus before the course.
Bibliography
- Billingsley, P. (2008). Probability and measure. John Wiley & Sons. [Casella and Berger, 1990] Casella, G. and Berger, R. L. (1990). Statistical inference, volume 70. Duxbury Press Belmont, CA.
- Cheng, S. (2008). A crash course on the lebesgue integral and measure theory.
- Durrett, R. (2010). Probability : theory and examples. Cambridge Uni- versity Press.
- Feller, W. (2008). An introduction to probability theory and its applications, volume 2. John Wiley &amp ; Sons.
- Lawler, G. F. (2011). An introduction to the mathematical foundations of probability theory.
- Pollard, D. (2002). A user's guide to measure theoretic probability, vo- lume 8 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge.
- Ross, S. and Peköz, E. (2007). A second course in probability. ProbabilityBookstore. com.
- Ross, S. M. (2010). A first course in probability. Pearson Prentice Hall. [Rudin, 2006] Rudin, W. (2006). Real and complex analysis. Tata McGraw-Hill Education.
- Van Gelder, P. (1996). A new statistical model for extreme water levels along the dutch coast. Stochastic Hydraulics, 96 :243-249.
- Williams, D. (1991). Probability with martingales. Cambridge university press.
Assessment methods and criteria
The exam will comprise two parts : an oral examination about the theory, and a written exam dedicated to the exercises. The balance will be around 40% for the oral exam and 60% for the written exam. A grade inferior to 6/20 in either of the parts will automatically lead to a failed mark for the course.
Work placement(s)
Organizational remarks
The course is taught in French.
Contacts
Yvik Swan Département de Mathématique, Grande Traverse, 12, Sart Tilman, B-4000 Liège +32 4 366 94 76 yswan at ulg.ac.be
Adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session
Teaching methods implemented : distance-learning
Assessment subjects
Assessment methods
The written exam will take place online (see calendar for the date and teacher informations for technical aspects).