Study Programmes 2015-2016
MATH0482-3  
Probability and statistics II
Duration :
30h Th, 15h Pr, 5h Mon. WS
Number of credits :
Bachelor in mathematics5
Lecturer :
Yvik Swan
Language(s) of instruction :
English language
Organisation and examination :
Teaching in the second semester
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
Course contents :
  • Probabilities on a finite set
  • Notions of measure theory
  • Random variables and random vectors
  • Expectation
  • Sequences of random vectors and convergence modes
  • The central limit theorem
  • Conditionnal expectation
  • Limit theorems
Learning outcomes of the course :
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 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 MyULg 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 first and second session exams will contain theoretical questions (some of which are announced in class) and exercises inspired by those studied during the year.  
Work placement(s) :
Organizational remarks :
Contacts :
Yvik Swan  Département de Mathématique, Grande Traverse, 12, Sart Tilman, B-4000 Liège +32 4 366 94 76 yswan at  ulg.ac.be