# Normal pdf

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The normal probability density function $f \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $\sigma^2>0$ by $$f(x)=\dfrac{1}{\sqrt{2\pi\sigma^2}} \exp \left(-\dfrac{(x-\mu)^2}{2\sigma^2} \right),$$ where $\pi$ denotes pi and $\exp$ denotes the exponential function.