Title of the course: Convergence, approximation and estimation in probability theory and statistics
Instructor: Dr. Serge Randriambololona
Institution: Lycée Claude Bernard
Dates: 11-17 August 2025
Prerequisites: Basic probability theory up to discrete and continuous random variables
Level: Undergraduate
Abstract: Given a sequence of random variables, there are various ways in which we can say that it converges. These various modes of convergence have applications to statistics.
We will 1) discuss relations between some of these modes of convergence, 2) state and prove the Weak Law of Large Numbers and De Moivre-Laplace theorem (a special case of the Central Limit theorem) and 3) consider some applications of the Weak Law of Large Numbers and the Central Limit Theorem to statistics, and 4) examine various approximation results involving binomial distributions, Poisson distributions and normal distributions.
Language: EN