  We will construct a confidence region of parameters for a sample of size $N$
from Cauchy distributed random variables. Although Cauchy distribution has two
parameters, a location parameter $\mu \in \mathbb{R}$ and a scale parameter
$\sigma > 0$, we will infer them at once by regarding them as a single complex
parameter $\gamma := \mu + i\sigma$. The region should be a domain in the
complex plane, and we will give a simple and concrete formula to give the
region as a disc and a square.
