Saint-Louis University - Bruxelles
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ECGE1132 - Descriptive Statistics and probability



Credits : 4

Lecturer :
Teaching assistants :
Mode of delivery :
Face-to-face , second term, 30 hours of theory and 22,5 hours of exercises.

Timetable :
Second term
Friday from 10:45 to 12:45 at 43 Botanique 1

Language of instruction :
The course and exercise sessions are given in French; the syllabus and exercise book are also written in French.

Learning outcomes :
The fundamental purpose of statistics is to identify, out a sample, results that are valid for the entire population. This inductive approach is called «Statistical Inference». At a preliminary stage, the sample should be simplified through its representation in graphs and charts, as precise as possible, without loosing too much information, and reduced to a few numbers that describe it. This is the role of Descriptive Statistics, which constitutes the first part of the course.

In order to go further than the simple description of the sample and to draw valid conclusions about the underlying population, additional hypothesis on the way in which the sample data has been generated, should be made. That is the role of the Theory of Probability, which provides the essential key to every inferential approach. This inductive approach introduces uncertainty; the theory of probability also enables to match any inferential conclusion with a reliability measure. The second part of the course will be an introduction to Probability.

The objective of the first part of the course is to familiarise the students with the primary tools of Descriptive Statistics, tools that they are confronted with on a daily basis through the media, which use them to excess. Besides its usefulness to describe an established fact or a sample, Descriptive Statistics allow an easy introduction to the Theory of Probability. The aim of the second part of the course is to introduce the students to the method of probabilistic reasoning. It is accompanied by examples in the field of economy and management that aim to illustrate the theory.

By the end of the course, the students should have acquired a sufficient ease in the understanding and manipulation of Descriptive Statistics and (simple) Probabilities to allow them to approach the Applied Statistics course in BLOC2. Descriptive Statistics and Probabilities are only the premises of this second course and are studied as such.


Prerequisites :
None

Co-requisites :
None

Course contents :
Introduction: (Syllabus, Chapter 1).

First Part: Descriptive Statistics: (Syllabus, Chapter 2).
1) Frequency distributions and Charts;
2) Distribution centre;
3) Dispersion of a distribution;
4) Linear Transformation;

Second Part: Theory of Probability
5) Probabilities: Frequency approach, Axiomatic approach and symmetric Probabilities, Conditional Probabilities (Syllabus, Chapter 3);
6) Probability Distributions: discrete case (Bernoulli, Binomial, Uniform, Poisson, Geometric and Hypergeometric distribution theories);
Density Functions: continuous case (Uniform, Normal and Exponential distribution theories) Random Variable Functions, Mathematic Expectation (Syllabus, Chapter 4);
7) Random Variables Coupling (discrete case): Joint, Marginal and Conditional distributions and their moments, Covariance, Correlation and Linear Combination of two random variables (Syllabus, Chapter 5).



Planned learning activities and teaching methods :
Lecture, tutorials, syllabus, exercise book and reference book(s), office hours

The lecture is a systematic initiation to the methodological foundations of Descriptive Statistics and to theoretical foundations of Probabilities; it is accompanied by examples that illustrate the theory. An effort is done throughout the course to involve the students in the discovery and development of new concepts and their applications. This active participation should enable the students to immediately engage in a research approach and to fully benefit from the exercise sessions that complete the lecture.

The active attendance to lectures and exercises sessions is highly recommended. This will greatly improve success chances.

The syllabus, the lecture and the exercise sessions form a whole: the different elements complete each other.

Tutorials are based on a collection of exercises (in continuous development) available at the syllabus desk. The assistant continues the new teaching method where open questions will be proposed to the students working in small subgroups. Each subgroup will send its collective work by email to the professor who will correct it and share it with the other subgroups. This way of functioning enables the students to discover (or rediscover) by themselves the fundamental concepts that punctuate the course and to acquire a certain dexterity in their manipulation. The assistant will set reception hours that the students are invited to comply with.



Assessment methods and criteria :
The written 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.


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

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

- Mendenhall W, Beaver R. J. and B. M. Beaver, Introduction to Probability and Statistics, Duxbury Press, 14 ed. 2012.

- Ross S. M., Initiations aux Probabilités, traduction de la 4ème édition américaine, Collection : Enseignement des Mathématiques, Presses polytechniques et universitaires normandes.

- Ross S., A first course in Probability, Pearson International Edition, 9th ed., 2013. ISBN-10: 1292024925.
- Wonnacott T. H. and R. J. Wonnacott, Statistique: Economie - Gestion - Sciences - Médecine (avec exercises d'application), Paris, Economica, 4ème ed. 2000.

- Howell D. C., Statistique en Sciences Humaines (M. Rogier, traduction française), Edition Deboeck, 2008.

- Bouget D. et A. Viénot, Traitement de l'Information : Statistique et Probabilités, Edition Vuibert, 1998.
américaine, Collection : Enseignement des Mathématiques, Presses polytechniques et universitaires normandes.



Other information :
A syllabus, an exercise book, a form, statistical tables, additional references.