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 also planned 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
• Elementary discrete models
• Random variables
• The expectation operator
• Classical probability distributions
• Univariate convergence of random variables

Part 1: Data analysis

The student will have to be able to present and interpret data in an adequate manner, in particular using the taught statistical software.

Part 2: Probability

At the end of the course the student will have a deep understanding of the concepts at the heart of probability theory. The student will know the fundamental probability distributions and will be able to competently perform probability computations. 

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 as well as in practical sessions organized in groups and on computers.
 

Part 2: Probability

Ex cathedra classes as well as exercise sessions.

Part 1: Data analysis

The lectures are organised face-to-face according to the official schedule. They will usually be recorded using the podcast system. The students may then watch the video when they wish.
 
The practicals are organised according to the official schedule given on Celcat. During these, the students are invited to interact with each other among a group. The groups will work on one personal computer (there is no need to have one computer per student; one computer per group of 3/4 students is enough).

Part 2: Probability

Lectures and practicals are organised face-to-face according to the official schedule.
Lectures could be recorded using the podcast system if required by the students.

Part 1: Data analysis

Lecture notes and slides will be available and put on eCampus, chapter after chapter.

Part 2: Probability

Lecture notes will be available.
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.

Part 1: Data analysis

This part of the course is evaluated by means of a pratical exam on a computer in order to check the good application of the techniques and the use of the software. The weight of this part will be specified in the overall description of the course.

Part 2: Probability

This part of the course will be assessed by an oral exam for the theory, and by a written exam for the exercises. Each part will represent at least 35% of the final note of this part of the course. The exact proportion for each part will be given when deemed appropriate.

Part 1: Data analysis

None

Part 2: Probability

All documents will be made available.

Part 1: Data analysis

G. HAESBROECK, Institut de mathématique, Bât B37, local 0/60, tél: 04/366-95-94, email: G.Haesbroeck@uliege.be
 S. KLENKENBERG, Institut de mathématique, Bât B37, email : s.klenkenberg@uliege.be

Part 2: Probability

A. DELIEGE, Institut Montéfiore, Bât B28, local I.72.b, tél: 04/366-27-19, email: adrien.deliege@uliege.be
G. HAESBROECK, Institut de mathématique, Bât B37, local 0/60, tél: 04/366-95-94, email: G.Haesbroeck@uliege.be
S. KLENKENBERG, Institut de mathématique, Bât B37, email : s.klenkenberg@uliege.be

Part 1: Data analysis

For this part of the course, only one practical could not be organised face-to-face. This practical has been organised on-line as follows: the practical statement was put on line just before the official time slot of the practical and the assistants were available during the practical to answer questions via a forum on eCampus.
As for the other practicals, a correction was made available at the end of the practical, this one taking the form of a video recorded by one assistant. 

Part 2: Probability

The theory is split into several audiovisual podcasts.
The exercise sheets are posted online. The students can ask their questions whenever they want. The answers to the exercises are provided afterwards.

Part 1: Data analysis

The content of the evaluation remains unchanged with respect to the information given at the beginning of the lectures.

Part 2: Probability

A table of content is provided. It contains the definitions, theorems, and proofs to study. The students must also be able to use these notions appropriately in exercises.

Part 1: Data analysis

The exam is replaced by a personnel project of data analysis using the software R. 
The project statement will be sent out on the 6th of May and the project (5 pages max) will have to be up-loaded on eCampus by the 20th of May at the latest. The R code will also be submitted. 
The institutional software "anti-plagiat" will be systematically applied to detect such type of behavior, which will then be sanctionned.

Part 2: Probability

A remote written exam will be organised, with the possibility of a remote oral exam, at the discretion of the teacher.

Part 1: Data analysis

The contatcs remain the same.

Part 2: Probability

A. DELIEGE, Institut Montéfiore, Bât B28, local I.72.b, tél: 04/366-27-19, email: adrien.deliege@uliege.be
G. HAESBROECK, Institut de mathématique, Bât B37, local 0/60, tél: 04/366-95-94, email: G.Haesbroeck@uliege.be
S. KLENKENBERG, Institut de mathématique, Bât B37, email : s.klenkenberg@uliege.be

Part 2: Probability

Same as May-June session.

Part 2: Probability

Same as May-June session.

Part 2: Probability

Same as May-June session.