Fiches de cours 2017-2018

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Probabilities and statistics

MATH-232

Enseignant(s) :

Davison Anthony C.

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.

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. 

Learning Prerequisites

Required courses

Analyse I, II

Algèbre linéaire

Learning Outcomes

By the end of the course, the student must be able to:

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