Probability & Statistical Inference · Probability Theory

Limit theorems of probability: Laws of large numbers and central limit theorem

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Probability theory · Advanced mathematical analysis

Overview

Topics covered

  • Introduction
  • Limit Theorems in Probability
  • Fundamentals of the convergence of random variables
  • Continuous Limit Theorem and Slutsky
  • Fundamental inequalities for asymptotic analysis
  • Borel-Cantelli lemmas and almost certain convergence

Related concepts

Main connections

  • Calculus & differentiation
  • Variance & standard deviation
  • Mean & expected value
  • Central limit theorem
  • Normal (Gaussian) distribution
  • Mathematical expectation & moments

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

ℙ({ω∈Ω:limn→∞Xn(ω)=X(ω)})=1.
View LaTeX source\P\left(\left\{\omega \in \Omega : \lim_{n\to\infty} X_n(\omega) = X(\omega)\right\}\right) = 1.