---
title: "joint probability distribution"
type: concept
related: [Baysian Network, Random Variables, Probability, Joint Probability Distribution]
source: https://www.jemoka.com/posts/kbhjoint_probability_distribution/
confidence: high
status: active
---

for random variables \(X, Y\), the joint probability distribution is the probability of both of them happening at once.
\begin{equation} p(x,y) \end{equation}
The most fundamental solution can be derived with a table where all complete probabilities are listed. They are going to be too large to practically store.
independent joint probability For any given variable, the probability of the joint of two separate events is their product.
probability of the joint of a Bayes Net \begin{equation} p(joint) = \prod_{i \in BN}^{} p(x_{i} | parents(x_{i})) \end{equation}
