Probability & Statistical Inference · Probability Theory

Probability theory · Convergence of random variables

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Mathematical theory of probability · Real analysis

Overview

Topics covered

  • Introduction
  • Convergence of Random Variables
  • Probability spaces and fundamental concepts
  • Almost Sure Convergence ( )
  • Borel-Cantelli Lemmas
  • Convergence in Probability ( )

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.

X−1(B)={ω∈Ω:X(ω)∈B}∈ℱ.
View LaTeX sourceX^{-1}(B) = \{\omega \in \Omega : X(\omega) \in B\} \in \mathcal{F}.