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

Second term
Friday from 10:45 to 12:45

The course is taught in French. The reference book is in English and the slides are in French ; they are however insufficient as course summary.

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 “In Depth Statistics” and “Econometrics” courses in the second and third years.
- 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

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The reference handbook: W. Mendenhall, D. Wackerly and R. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, 7th edition, 2008.

- Introduction to statistics (MWS, Chapter 1);
- Probabilities (MWS, Chapter 2);
- Discrete random variables (MWS, Chapter 3);
- Continuous random variables (MWS, Chapter 4);
- Multivariate variables (MWS, Chapter 5);
- Functions of random variables (MWS, Chapter 6);
- Sampling and “central-limit” theorem (MWS, Chapter 7);

Lecture and tutorials.
a) The lecture is a systematic initiation to theoretical and methodological foundations of probabilities ans its probabilistic mode of reasonning. In addition to the intuitive explanations of the subject, the lecture focuses on manipulations and formalized concepts that allow a rigorous knowledge of the calculation of probabilities. It is accompanied by concrete examples notably chosen in the field of economics but also in the fields of interest of the management engineer intended to illustrate and apply the theory. A special effort is made throughout the course to involve the students in the discovery and formulation of new statistical concepts and their applications. This active participation to the sessions should enable the students to fully benefit from the tutorials that complete the lecture and also to wholly engage in a research approach.


The course is supported by a reference book.

b) Tutorials, are based on a collection of exercises available at the reference book. He will set reception hours that the students are invited to comply with.

c) Active attendance to lectures and tutorials is highly recommended; this will greatly improve chances of success. But
a personal work is also essential to pass the exam. Regular work (including solving exercises) is compulsory from the first week on. The students have to spent enough time for understanding deeply the course material and for achieving suffisant skills. So the personal work does'nt consist in learning by heart.

Other reference books, mainly available at the Faculty library, will be proposed to the students, for additional information, for their more or less formalized aspect and/or their range of solved or unsolved exercises.

The assessment is a closed book written examination.
The examination is held during the last two exam sessions in the following manner: The whole exam lasts three hours. During the first part (1h30), the student will be assessed on his understanding of the course, requiring personal reflection on the entire subject matter. The second part (1h30) will be devoted to solving exercises. Each part counts for ½ of the final mark.

The students will be entitled to use a form, statistical tables and their calculator (not alphanumeric).

Remark:
This course outline is subject to change: Throughout the sessions, depending on the group dynamic with the students, and from year to year through improvements brought to the course.
- 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 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.
(http://www.colorado.edu/economics/morey/7818/MoodGraybillBoesBook/MGB3rdSearchable.pdf)

- Rohatgi V. K. and A. M. Md. Ehsanes Saleh, Introduction to probability and Statistics, Wiley-Interscience; 2d ed., 2000.

- Ross S., A first course in Probability, Pearson International Edition, 9th ed., 2013. ISBN-10: 1292024925.

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

The course is compulsory for the students in Management Engineering.
- The course is recommended for students looking for an in depth training in statistics.
- This course is part of a logical progression in statistical training. It is followed by the “In depth statistics » and econometrics” course in BLOC 2 and BLOC 3, resp.
- The course is to be avoided by students experiencing difficulties in mathematics.