Normal Distribution.md

Normal Distribution

If a probability density function is the [[Standard Normal Distribution]] in standard coordinates, it is a [[Normal Distribution]] $$p(x)=\left(\frac{1}{\sigma\sqrt{2\pi}}\right)\exp\left(\frac{-(x-\mu)^2}{2\sigma^2}\right)$$ We then by definition have: $$\begin{align*}\mu&=\mu\\sigma^2&=\sigma^2\end{align*}$$ Note that

• 68% of the time, normal random variable within one standard deviation of mean
• 95% of the time, normal random variable within two standard deviations of mean
• 99% of the time, normal random variable within three standard deviations of the mean