Probabilities and statistics (I)

Teacher(s)

Bogaert Patrick;

Language

French

Prerequisites

Préalabre : LBIR1110

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.

Learning outcomes

At the end of this learning unit, the student is able to :
1	a.     Contribution of this activity to the learning outcomes referential : 1.1, 2.1 b.     Specific formulation of the learning outcomes for this activity A 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

Online resources

Moodle

Teaching materials

• P. Bogaert (2020). Probabilités pour scientifiques et ingénieurs (2ème éd). Editions De Boeck.

Faculty or entity

> AGRO