# Tronc CommunMathematicsProbability theory and Statistics

Lecturer(s): Marie-Christophette BLANCHET, Céline HARTWEG-HELBERT
Course ⋅ 14 hTC ⋅ 16 h

## Objectives

This first part of the course deals with the modelling with random variables. We introduce the notion of density. Some methods of probability calculus, approximations and asymptotic theorems are studied. A important part of the course is devoted to the numerical simulation with MATLAB. The second part of the course deals with statistics. The notions of estimators and tests are introduced. A chapter is devoted to linear regression.

## Palabras clave

Probability law, random variables, gaussian vectors, Monte-Carlo method, estimators, biais, statistic tests, linear regression.

## Programme

Probability : (1) Random Variables (2) Mean and variance (3) Random vectors (4) Random variables sequences- Asymptotic results- Monte-Carlo method.

Statistic : (5) Estimation (6) Estimation by confidence intervalle (7) Statistic tests(8) Linear regression

## Learning Outcomes

• Be able to compute probabilities.
• Be able to simulate random varaibles with Matlab
• Be able to estimate some parametres of law from data.
• Be able to construct and analyse a linear regression.

## Assesment

Final mark = 75% Knowledge + 25% Know-how Knowledge mark = 100% final exam Know-how mark = 100% continuous assessment