Probability

Objectifs

Master the notion of conditional expectation, for intensive use in second-year regression and econometrics courses,

Use the different modes of convergence of a series of random variables without difficulty, a prerequisite for any statistics course with a mathematical aspect.

Plan

Conditional expectation: expectation conditional on an event, expectation conditional on a random variable. Construction of conditional expectation by orthogonal projection, general definition.

Stochastic convergence: convergence in law, convergence in probability, convergence in Lp, almost certain convergence. Relationships between these convergences. Law of large numbers, central limit theorem, asymptotic confidence interval.

Prérequis

Probability and integration courses for the 1st semester of the first year at school