Face-to-face , second term, 30 hours of theory and 22,5 hours of exercises.

Second term
Friday from 14:00 to 16:00 at 109 Marais 301

The course is taught in French. The reference book is in English.

General objectives:
- To introduce to the probabilistic way of thinking and to the statistical analysis methods. These methods are useful in every scientific field where random and/or experimental aspects occur (human, technical, medical or natural sciences). The course will especially develop the tools useful for management and economic sciences.
- This course is in line with a training in statistics. It is usually followed by the “Extensive Statistics”, “Multivariate Statistics” and “Econometrics” courses in the second year.
- The course is to be avoided by students having difficulties in mathematics.

Specific objectives:
By the end of the Probabilities course, the students should be able:
- to understand and model random aspects of some phenomena;
- to correctly model simple experiences (draw with our without replacement) and calculate the probabilities of events of interest;
- to apply these fundamental models to real situations (gambling...);
- to describe a random experience using uni- and bivariate random variables;
- to use discrete and continuous random variables to calculate probabilities in real problems;
- to study the properties of random variable functions.

None

None

- Introduction to statistics;
- Probabilities;
- Discrete random variables;
- Continuous random variables;
- Multivariate variables;
- Functions of random variables;
- Sampling and “central-limit” theorem.

Lecture and tutorials.

The assessment is a closed book written examination:
- the examination questions (about 75%) are similar to the exercises (completed or not during tutorials) and examples of the manual;
- these questions will be completed by other, more theoretical questions (25%) ;
- the students will have at their disposal a form including the main discrete and continuous probability principles studied in class and their main properties (moments...), as well as a general form prepared by the professor. These formulas can be found at the end of the syllabus of slides;
- the useful statistical tables will also be available.

Active attendance to lecture and tutorials is highly recommended. Regular work (solving of exercises) is compulsory from the first week on, otherwise, there will be no hope of passing the examination.

Wackerly D. D., Mendenhall W and R.L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, 7th ed., 2008.

Mood A.M., Graybill F.A. and D.C. Boes, Introduction to the Theory of Statistics, Mc Graw Hill Ed., 1974.

Comte M. et J. Gaden, Statistiques et Probabilités pour les sciences économiques et sociales, Collection Mayor, PUF, 1ère édition, 2000.

This course, as well as the “Extensive Statistics” course, is based on the following book (available at the syllabus service):
Wackerly D. D., Mendenhall W and R.L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, 7th ed., 2008.
- chapters 1 to 7 constitute the subject matter of the Probabilities course;
- chapters 7 to 14 constitute the subject matter of the Extensive Statistics course.
Slides (prepared by Professor Johan Segers, UCL) will be used in class. A copy of these slides will be available for the students. They are however insufficient as course summary.