Probability and statistics

Objectifs

Objectives:
At the end of this module, the student will 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 by Bayes formula
- to determine the law of a given random variable, to
compute its expectation, variance, characteristic
function, etc ¿
- to prove independence between random variables
(when they are independent)
- to approximate distributions by using underlying
limit theorems
- to estimate by confidence intervals some unknown
parameters (expectation, variance, proportion)
associated to a large population

Pré-requis

Necessary knowledge:
Lectures of mathematics of first year (I1ANMAAR, I1ANMATC, I1ANMAEF).
Lectures of mathematics of second year (I2MIMT11, I2MIMT21)

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…