---
title: "normal random variable"
type: concept
related: [Parameter, Normal Random Variable, Random Variables]
source: https://www.jemoka.com/posts/kbhnormal_random_variable/
confidence: high
status: active
---

normal random variable is a continuous random variable that allows you to manually specify the expectation and variance
constituents \(\mu\) the mean \(\sigma\) the variance requirements \begin{equation} X \sim \mathcal{N}(\mu, \sigma^{2}) \end{equation}
PDF:
\begin{equation} f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x-\mu)^{2}}{2 \sigma^{2}}} \end{equation}
additional information normal maximizes entropy no other random variable uses as little parameters to convey as much information
