Second semester

Probability (ES)

Teacher(s): Guillaume CHAUVET, Céline GAUTHIER, Antoine POINTEAUX

Course type: STATISTICS

Correspondant: Adrien SAUMARD

Unit: Module 1-06-M-E-S: Inferential Statistics

Number of ECTS: 1

Course code: 1ASTA08-ES

Distribution of courses

Heures de cours : 10.5

Heures de TP : 12

Language of teaching: French

Evaluation methods: examen écrit

Objectives

Master the concept of conditional expectation, with a view to its intensive use in second-year regression and econometrics courses. Easily use the different modes of convergence of a sequence of random variables, a prerequisite for any statistics course with a mathematical component.

Course outline

Conditional expectation: expectation conditional on an event, expectation conditional on a random variable. Construction of conditional expectation by orthogonal projection, general definition. Stochastic convergences: convergence in distribution, convergence in probability, convergence in Lp, almost certain convergence. Relationships between these convergences. Law of large numbers, central limit theorem, asymptotic confidence interval.

Prerequisites

Probability and integration courses for the first semester