# Coursebooks

## Probability theory

#### Lecturer(s) :

Chong Carsten Hao Ye

English

#### Summary

The course provides a measure-theoretic introduction to probability.

#### Content

- general probability spaces, random variables and measurable functions, measures and probabilities

- expectation for a random variable and reminder of integration theory

- independence and the Borel-Cantelli lemmas

- strong and weak laws of large numbers

- central limit theorem

#### Learning Prerequisites

##### Recommended courses

First cycle, Advanced analysis A (measure theory)

#### Learning Outcomes

By the end of the course, the student must be able to:
• Define a probability space
• Define various modes of convergence
• Characterize convergence in distribution
• Analyze tail events via the Borel Cantelli Lemmas

#### Teaching methods

Ex cathedra lecture and exercises in the classroom

#### Assessment methods

Exam written

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

#### Supervision

 Office hours No Assistants No Forum No

#### Resources

##### Bibliography

R. Durrett. Probability: theory and examples.

#### Prerequisite for

Probabilities, Stochastic process

### In the programs

• Applied Mathematics, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics for teaching, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics for teaching, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
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
Under construction
Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German