Fiche de cours

Probability and statistics

MATH-232

Fiche de cours

Enseignant(s) :

Abbé Emmanuel
Berthier Raphaël Jean

Langue:

English

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.  

Prerequisite for

Electrométrie, Théorie du signal, Télécommunications, Information et codage, Fiabilités, ...