Probability and statistics
Summary
A basic course in probability and statistics
Content
Revision of basic set theory and combinatorics.
Elementary probability: random experiment; probability space; conditional probability; independence.
Random variables: basic notions; density and mass functions; examples including Bernoulli, binomial, geometric, Poisson, uniform, normal; mean, variance, correlation and covariance; moment-generating function; joint distributions, conditional and marginal distributions; transformations.
Many random variables: notions of convergence; laws of large numbers; central limit theorem; delta method; applications.
Statistical inference: different types of estimator and their properties and comparison; confidence intervals; hypothesis testing; likelihood inference and statistical modelling; Bayesian inference and prediction; examples.
Learning Prerequisites
Required courses
Analyse I, II
Algèbre linéaire
Teaching methods
Ex cathedra lectures, exercises and problems
Assessment methods
Mid-term and final exams
Resources
Bibliography
Ross, S. (2012) A first course in probability (9th edition). Pearson.
Aussi disponible en traduction française (PPUR): `Initiation aux probabilités'.
A polycopié of the course notes, with the problems etc., will also be available.
Ressources en bibliothèque
Prerequisite for
Electrométrie, Théorie du signal, Télécommunications, Information et codage, Fiabilités, ...
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Probability and statistics
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Probability and statistics
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Probability and statistics
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Probability and statistics
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Probability and statistics
- Cours: 4 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines