Let X1 , , Xn be independent and identically distributed Cauchy random variables with unknown parameters (, ). Let X and s 2 X be

Let X1

, …, Xn be independent and identically distributed Cauchy random variables with unknown parameters (θ, τ). Let X̄ and s 2

X be the sample mean and sample variance respectively. By writing Xi = θ + τεi

, show that the joint distribution of the configuration statistic A with components Ai = (Xi − X̄)/sX is independent of the parameters and hence that A is ancillary. [This result applies equally to any locationscale family where the εi are i.i.d. with known distribution.]