---
title: "conditional Gaussian model"
source: https://www.jemoka.com/posts/kbhconditional_gaussian_models/
---

Say you have one continuous variable \(X\), and one discrete variable \(Y\), and you desire to express the probability of \(X\) conditioned upon \(Y\) using a gaussian model:
\begin{equation} p(x|y) = \begin{cases} \mathcal{N}(x \mid \mu_{1}, \sigma_{1}^{2}), y^{1} \\ \dots \\ \mathcal{N}(x \mid \mu_{1}, \sigma_{1}^{2}), y^{n} \\ \end{cases} \end{equation}
