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Probability and statistics

Objectives

At the end of the module, the student will have understood and be able to explain :
 
-what a probability space is
- the notion of conditional probability and independence between events
- what a random variable (discrete or continuous) and its characteristics are
- how to apply limit theorems such as the Law of Large Numbers (LLN) or the Central
Limit Theorem (CLT)
- the notion of statistical estimation
The student will be able :
- to compute probabilities using Bayes formula
- to determine the law of a given random variable, to compute its expectation, variance,
characteristic function, etc...
- to prove independence between random variables (when they are independent)
- to approximate distributions by using underlying limit theorems
- to estimate, using confidence intervals, unknown parameters (expectation,
variance, proportion) associated with a large population

Needed prerequisite

Lectures of mathematics of first and second years (integral calculus...)

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...