Probability

Part 1: Data analysis

This part of the course is devoted to the recall of statistical concepts taught in secondary school as well as to the presentation of some extensions. The learning of a statistical software is strongly recommended to students for the practical implementation of the concepts discussed in this part.

Part 2: Probability

This part of the course is devoted to the learning of the basis of probability theory. The table of contents is the following:

• Probability spaces 
• Random variables 
• The expectation operator 
• Classical probability distributions 
• Convergence of random variables
• Point estimation and confidence intervals
• Introduction to statistical tests

Part 1: Data analysis

The student will have to be able to present and interpret data in an adequate manner.

Part 2: Probability

At the end of the course the student will have an understanding of the concepts of probability theory and their application to statistical infernce. 

Part 1: Data analysis

The statistical techniques included in the official program of secondary school in Belgium are assumed to be known but some additional notes will be available for students who need to revise these notions.

Part 2: Probability

A good mastery of elementary calculus is indispensable to follow this class.

Part 1: Data analysis

The course is concentrated in 3 ex-cathedra lectures.

Part 2: Probability

Ex cathedra classes as well as exercise sessions.

Part 2: Probability

• 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. 

Part 1: Data analysis

Any session :

- In-person

written exam ( multiple-choice questionnaire, open-ended questions )

- Remote

written exam

- If evaluation in "hybrid"

preferred in-person

Part 2: Probability

Any session :

- In-person

written exam ( multiple-choice questionnaire, open-ended questions )

- Remote

written exam

- If evaluation in "hybrid"

preferred in-person