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; |

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] in Data Science : Statistic

Minor in Statistics, Actuarial Sciences and Data Sciences

Interdisciplinary Advanced Master in Science and Management of the Environment and Sustainable Development

Master [120] in Environmental Science and Management