Probability theory
Summary
The course is based on Durrett's text book Probability: Theory and Examples. It takes the measure theory approach to probability theory, wherein expectations are simply abstract integrals.
Content
(i) Definitions of probability space and random variables
(ii) independence
(iii) Different types of convergence for random variables.
(iv) Weak laws of large numbers
(v) Borel Cantelli Lemmas and Strong Law of large numbers
(vi) 0-1 laws
(vii) Convergence in law
(vi) Lindeberg-Feller CLT.
Keywords
sigma field
random variable
measurable
convergence a.s.
independence
Learning Prerequisites
Required courses
None but it helps to be familiar with measure threory.
Teaching methods
blackboard lectures
Assessment methods
Mostly the final exam but also exercises.
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Probability theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Probability theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Probability theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
Semaine de référence
| Lu | Ma | Me | Je | Ve | |
| 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 |
Légendes:
Cours
Exercice, TP
Projet, autre