Probabilités et statistiques

Probability:

1. Probability calculus (definitions, elementary properties, uniform probability, conditional probability, independence);
2. Random variables (motivation and definition; discrete r.v., continuous r.v., expectations, variances and other moments);
3. Random models (fundamental experiments, discrete random models, continuous random models);
4. Multivariate models (joint mass, density and distribution functions, marginal laws, conditional laws, independence, expectations of random vectors, conditional expectation);
5. Some limit theorems (law of large numbers, central limit theorem).

Statistics:

1. Estimators, confidence intervals;
2. Hypothesis tests for a proportion, a mean, a comparison of 2 proportions or 2 means;
3. Chi-square tests for goodness-of-fit, homogeneity, and independence;
4. Simple linear regression model;
5. Analysis of variance.

The course will begin with the "Probability" part, which will provide the tools necessary to understand the second part of the course, which deals with Statistics topics.

The teaching unit (UE) aims to provide students with probability and statistics methods that will allow them to handle the datasets they will encounter later in their studies or career. In particular, this UE will help the student refine the conclusions they can draw from an experiment or a survey, and will help them choose a statistical method based on (i) the dataset they are dealing with, and (ii) their objectives. The course will be illustrated with numerous examples.

For the part devoted to probability, by the end of this teaching unit a student will be able to:

1°) Calculate probabilities in a univariate and multivariate, discrete and continuous setting;
2°) Use Bayes' theorem and the law of total probability to calculate the probabilities of dependent events;
3°) Calculate the expectation and variance of discrete and continuous random variables in a univariate and multivariate setting;
4°) Assign a probability distribution to real-world events, in order to calculate the corresponding probabilities and moments;
5°) Use the law of iterated expectations and apply it to stochastic sums;
6°) Identify applications of the law of large numbers and the central limit theorem.

For the part devoted to statistics, the UE will enable the student to:

1°) Produce an appropriate point estimate;
2°) Correctly identify the test to apply in a practical situation;
3°) Construct a confidence interval for the parameter of interest;
4°) Analyze the relationships between several variables.

Required and Corequired knowledge and skills

MATHF112 and MATHF114 for BA-INFO

Required and corequired courses

Courses requiring this course

The course will be taught at the blackboard and using slides. In the Statistics part, problem-based learning will be used. Students will be presented with one or more situations in which they must apply a test. Active learning activities will be implemented. Information relating to the course will be available on the instructors' personal webpages as well as on the virtual university platform.

Attendance at both the lectures and the exercise sessions is strongly recommended.

The course is taught in French.

References, bibliography, and recommended reading

Probability: course notes for Part 1 on sale at the PUB and available in PDF format on the virtual university (UV).

Statistics: Course notes. These may be supplemented by reading introductory statistics textbooks.

"Éléments de Statistique." C. Dehon, J.-J. Droesbeke, C. Vermandele, published by Université Libre de Bruxelles and Ellipses.

Course notes

• Podcast
• Syllabus
• Université virtuelle

Contacts

Probability section & coordination: Jennifer Alonso García, email: jennifer.alonso.garcia@ulb.be; office: Plaine campus, NO building, room 2.09.116
Statistics section: Thomas Verdebout, email: thomas.verdebout@ulb.be; office: Plaine campus, NO building, room 2.O9.114

Campus

Plaine

Method(s) of evaluation

• written examination

written examination

Conditions permitting, evaluation will take place solely through a written exam in January, covering both parts. This may be revised at any time depending on health/sanitary conditions.
The exam combines theoretical questions and exercises for both parts.

Mark calculation method (including weighting of intermediary marks)

The final grade will be based on the written exam held after the course.

Language(s) of evaluation

• french