Overview

In this section, we study the interactions between multiple random variables. We define independence rigorously, explore how distributions behave jointly, and introduce powerful tools like characteristic functions to analyze sums and limits of random variables.

Key Topics

1. Independence of Random Variables: Formal definition and criteria for independence.
2. Joint Distribution: How multiple random variables are distributed together, including marginal and conditional distributions.
3. Covariance: Measuring the linear dependence between two random variables.
4. Characteristic Function: The Fourier transform of a distribution—a fundamental tool for proving limit theorems.
5. Multivariate Gaussian: The most important joint distribution in probability and statistics.