Due to the COVID-19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).

Teacher(s)

Language

French

Prerequisites

LBIR1110

LBIR1111

LBIR1111

*The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.*
Main themes

Introduction to the calculus of probability - Discrete and continuous random variables: probability and probability density functions, expectations, variance and other statistical properties - Principal statistical distributions - Couples of random variables and random vectors: joint, marginal and conditional distributions, independence, covariance and correlation, expectations and conditional variance - Introduction to statistics - Notions concerning estimators and estimator properties - Inference about the mean and variance: estimators, sample distributions - Notions of one-mean-confidence intervals.

Aims

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a. Contribution of this activity to the learning outcomes referential :1.1, 2.1 b. Specific formulation of the learning outcomes for this activityA the end of this activity, the student is able to : · Name, describe and explain the theoretical concepts underlying the probability theory; · Use the mathematical expressions in a formal way and by using rigorous notations in order to deduce new expressions or requested theoretical results; · Translate mathematically textual statements using a rigorous mathematical and probabilistic framework by relying on appropriate concepts and theoretical tools; · Solve an applied problem by using a deductive approach that relies on a correct use of well identified properties and expressions; · Validate the internal consistency of the mathematical expressions and results based on theoretical properties and logical constraints that are induced by the probabilistic framework; |

*The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.*

Content

Introduction to the calculus of probability - Discrete and continuous random variables: probability and probability density functions, expectations, variance and other statistical properties - Principal statistical distributions - Couples of random variables and random vectors: joint, marginal and conditional distributions, independence, covariance and correlation, expectations and conditional variance - Introduction to statistics - Notions concerning estimators and estimator properties - Inference about the mean and variance: estimators, sample distributions. Notion of confidence intervals.

Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Regular courses and supervised practical exercises
Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Evaluation: Open book written examination (only with the original material). The examination is composed of exercises to be solved. Its duration is about 3 hours.
Other information

The course relies on a book which is considered as mandatory and must be bought :

P. Bogaert (2005). Probabilités pour scientifiques et ingénieurs. Editions De Boeck

P. Bogaert (2005). Probabilités pour scientifiques et ingénieurs. Editions De Boeck

Online resources

Moodle

Faculty or entity

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme

Sigle

Credits

Prerequisites

Aims

Master [120] en science des données, orientation statistique

Mineure en statistique, sciences actuarielles et science des données

Master de spécialisation interdisciplinaire en sciences et gestion de l'environnement et du développement durable

Master [120] en sciences et gestion de l'environnement