Probability-Statistics

Description

Objectifs

At the end of this module, the student should have understood and be able to explain (main concepts):

- what a probability space is
- the notion of conditional probability and
independence between events
- what a random variable (discrete or continuous)
and its characteristics are
- how to apply limit theorems such as the Law of
Large Numbers (LLN) or the Central Limit Theorem
(CLT)
- the notion of statistical estimation

The student will be able to: 

- to compute probabilities using Bayes formula
- to determine the law of a random variable, to
compute its expectation, variance, cumulative distributive and characteristic
functions, etc
- to study the independence of random variables
- to approximate distributions by using underlying
limit theorems
- to estimate using confidence intervals some unknown parameters (expectation, variance, proportion) associated to a large population

Pré-requis

Basic set theory, summations and series, derivation, integration (both simple and multiple), improper integrals, equivalents and limit computations.

Évaluation

L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…