Teacher(s)

Language

French

Prerequisites

Préalabre : LBIR1110

Prérequis : LBIR1111

Prérequis : 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

Notion of event and probability - Major theorems of probability calculus. Discrete and continuous random variables: probability and probability density functions, expectations, variance and other statistical properties. Major univariate statistical distributions. Couples of random variables and random vectors: joint, marginal and conditional distributions, independence, covariance and correlation, expectations and conditional variance. Introduction to random numbers and their applications.

Teaching methods

Regular courses and supervised practical exercises

Evaluation methods

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 (2020). Probabilités pour scientifiques et ingénieurs (2nd ed). Editions De Boeck

P. Bogaert (2020). Probabilités pour scientifiques et ingénieurs (2nd ed). 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

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

Master [120] in Data Science : Statistic