Program (detailed contents):
– Probability spaces
– Conditional probability and independence
– Random variables (discrete or continuous) and their characteristics
– Multidimensional random variables, conditional distributions and independence
– Limit theorems (LLN and CLT) and approximation of laws
At the end of this module, the student should have understood and be able to explain (main concepts): - 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) - 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
- what a probability space is
The student will be able to:
Basic set theory, summations and series, derivation, integration (both simple and multiple), improper integrals, equivalents and limit computations.
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…
Crédits ECTS :
Nombre d’heures : 26.0
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Dans un souci d'alléger le texte et sans aucune discrimination de genre, l'emploi du genre masculin est utilisé à titre épicène.