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

Second term
Friday from 09:00 to 11:00 at 109 Marais 100

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

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.

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 Statistical Analysis course in BAC2. Descriptive Statistics and Probabilities are only the premises of this second course and are studied as such.

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Introduction: (Chapter 1).

First Part: Descriptive Statistics: (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 (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 (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 (Chapter 5).

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.

The final evaluation will be a written examination, organised in three sessions in the following manner: The whole exam lasts three hours. During the first hour, the student will be assessed on his understanding of the course, requiring personal reflection on the entire subject matter. The two following hours will be devoted to solving exercises. The first part counts for 1/3 of the final mark, and the second part counts for the remaining 2/3 of the final mark.

The students will be entitled to use the form mentioned here above, the statistic tables and their calculator (not alphanumerical).

Remark:
This course outline is subject to change: according to the progress of the course, to the dynamic with the students, and over time, by improvements brought to the course.

- 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, 13th édition. Brooks/Coles, USA, 2009.

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

- Ewald Fr., Histoire de l'Etat providence, Ed. Grasset et Fasquelle, 1996.

- Ross S., A First Course in Probability, Pearson Prentice Hall, 7th ed., 2006.

- Hacking I., L'émergence de la probabilité, Collection Liber, Ed. Seuil, 2002.

- Hacking I. et M. Dufour, L'ouverture au probable : éléments de logique inductive, Ed. Armand Colin, Paris, 2004.

- Wonnacott T. H. et R. J. Wonnacott, Statistique : Economie - Gestion - Sciences - Médecine (traduction française), Paris, Economica, 4ème ed., 2000.

- Howell, Statistique en Sciences Humaines (traduction française), Edition Deboeck, 1998.

- Bouget D. et A. Viénot, Traitement de l'Information : Statistique et Probabilités, Edition Vuibert, 1995.

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