# Stein's method and the distribution of the product of zero mean correlated normal random variables

## TL;DR

This paper introduces a new proof using Stein's method to derive the distribution of the product of two zero-mean correlated normal variables, providing a clearer approach to a classical problem.

## Contribution

It presents a novel application of Stein's method to derive the distribution of the product of correlated normal variables, offering a simpler proof and methodological insights.

## Key findings

- New proof of the distribution formula
- Methodology applicable to related problems
- Enhanced understanding of product distribution

## Abstract

Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a recent technique from the Stein's method literature to obtain a simple new proof, which also serves as an exposition of a general method that may be useful in related problems.