# Coursebooks

## Probabilities and statistics

Abbé Emmanuel

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.

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

#### 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.

#### Prerequisite for

Electrométrie, Théorie du signal, Télécommunications, Information et codage, Fiabilités, ...

### In the programs

• Semester
Spring
• Exam form
Written
• Credits
6
• Subject examined
Probabilities 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
• Credits
6
• Subject examined
Probabilities and statistics
• Lecture
4 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Passerelle HES - IN, 2019-2020, Spring semester
• Semester
Spring
• Exam form
Written
• Credits
6
• Subject examined
Probabilities and statistics
• Lecture
4 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Passerelle HES - SC, 2019-2020, Spring semester
• Semester
Spring
• Exam form
Written
• Credits
6
• Subject examined
Probabilities and statistics
• Lecture
4 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
8-9   CM3
9-10
10-11   CO3
11-12
12-13
13-14 CO3
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Lecture
Exercise, TP
Project, other

### legend

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