Probabilities

Objectives

The aim of this course is to enable the future engineer to build a mathematical model based on the observation of a random phenomenon and a collection of experimental or sampling data. This construction goes from the choice of model to its precise adjustment and its validation. This model must then allow a better understanding or analysis of the phenomenon and lead, if necessary, to decision-making or forecasts.

Description

1st course: Probability in infinite and uncountable spaces.
2nd course: Real random variables; basic concepts ; discrete distributions.

3rd course: Real random variables; probability density functions.
4th course: End of random variables; change of variable. Random vectors.
5th course: Correlation; marginal distributions; Independence. Change of variables. 6th course: Characteristic function. Convergences. Law of large numbers. 7th course: Complements; revisions. Tutorials

TD 1: Probability derivation.

TD 2: The discrete distributions.

TD 3: The continuous distributions.

TD 4: Bivariate change of variables.

TD 5: Characteristic function; Convergences. Practical work

TP 1 and 2: Initiation to Matlab for probabilities and statistics.

TP 3 and 4: Simulation of random variables.

Bibliography

Combrouze, A et Deyde, A. (1996) : Probabilités et statistiques. PUF.

Garel, B. (2002) : Modélisation probabiliste et statistique. Cépadues Editions.

Garel, B. (2018) : Modèles mathématiques du hasard. Ellipses.

Méléart S. (2010) : Introduction à la théorie et au calcul des probabilités. Ecole Polytechnique, Paris.

Session 1 ou session unique - Contrôle des connaissances

Session 2 - Contrôle des connaissances