# Fiches de cours 2017-2018

## Probabilities and statistics

#### Enseignant(s) :

Davison Anthony C.

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.

Descriptive statistics: basic graphs and statistics; notions of robustness.

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.

Analyse I, II

Algèbre linéaire

#### Learning Outcomes

By the end of the course, the student must be able to:
• Construct confidence intervals for inference under uncertainty
• Contrast probability models and data
• Derive probabilities and other properties of random samples
• Compute probabilities based on simple combinations of logical statements
• Infer characteristics of probability models from empirical data
• Compute measures of location, scale and association for simple datasets
• Formulate probability models appropriate for simple problems
• Interpret data through simple graphics

#### Teaching methods

Ex cathedra lectures, exercises and problems

#### Assessment methods

Quizzes, mid-term test, final exam

#### Supervision

 Office hours No Assistants Yes Forum Yes

#### 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, ...

### Dans les plans d'études

• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
6
• Matière examinée
Probabilities and statistics
• Cours
4 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Passerelle HES - IN, 2017-2018, Semestre printemps
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
6
• Matière examinée
Probabilities and statistics
• Cours
4 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Passerelle HES - SC, 2017-2018, Semestre printemps
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
6
• Matière examinée
Probabilities 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
• Crédits
6
• Matière examinée
Probabilities and statistics
• Cours
4 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines

### Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
En construction

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand