Cauchy pdf
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The Cauchy probability density function $f \colon \mathbb{R} \rightarrow \mathbb{R}$ for $x_0 \in \mathbb{R}$ and $\gamma >0$ is given by $$f(x) = \dfrac{1}{\pi \gamma \left[1 + \left( \frac{x-x_0}{\gamma} \right)^2 \right]},$$ where $\pi$ denotes pi.
