# An Inequality for the Correlation of Two Functions Operating on Symmetric Bivariate Normal Variables

## TL;DR

This paper derives a simple inequality relating the correlation of two functions of symmetric bivariate normal variables, based on the Cauchy-Schwarz inequality, providing theoretical insight into their dependence structure.

## Contribution

It introduces a new inequality for the correlation of functions of symmetric bivariate normal variables, expanding understanding of their dependence.

## Key findings

- The inequality is a direct consequence of the Cauchy-Schwarz inequality.
- It provides bounds on the correlation of transformed variables.
- The result enhances theoretical understanding of symmetric bivariate normal functions.

## Abstract

An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.