Probability & Statistical Inference · Probability Theory

Probability · One-dimensional random variables

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Advanced Probability Theory · Analysis of Random Variables

Overview

Topics covered

  • Introduction
  • One-Dimensional Random Variables
  • Probability space and definition of random variable
  • Measurability and its Analytical Justification
  • The Induced Probability Measure
  • Cumulative Distribution Function (CDF)

Related concepts

Main connections

  • Calculus & differentiation
  • Mathematical expectation & moments
  • Measure theory & Lebesgue integration
  • Variance & standard deviation
  • Normal (Gaussian) distribution
  • Median & robust location

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,∀B∈ℬ(ℝ).
View LaTeX sourceX^{-1}(B) = \{ \omega \in \Omega : X(\omega) \in B \} \in \F, \qquad \forall B \in \B(\R).