# 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, ...

## In the programs

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Probability and statistics**Lecture:**4 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Probability and statistics**Lecture:**4 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Probability and statistics**Lecture:**4 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Probability and statistics**Lecture:**4 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Probability and statistics**Lecture:**4 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks