---
title: "continuous distribution"
type: concept
source: https://www.jemoka.com/posts/kbhcontinuous_distribution/
confidence: high
status: active
---

This is a continuous distribution for which the probability can be quantified as:
\begin{equation} p(x) \dd{x} \end{equation}
You will note that, at any given exact point, the probability is \(\lim_{\dd{x} \to 0} p(x)\dd{x} = 0\). However, to get the actual probability, we take an integral over some range:
\begin{equation} \int_{-\infty}^{\infty} p(x) \dd{x} = 1 \end{equation}
See also cumulative distribution function which represents the chance of something happening up to a threshold.
