Consider the Cauchy density f(x) = 1 π(1+x2) , x ∈ R. Find the MLE of θ for a sample size 3 from the Cauchy density f(x−θ), and discuss whether it has a finite first moment or not. Is there any...

Consider the Cauchy density f(x) = 1 π(1+x2) , x ∈ R. Find the MLE of θ for a sample size 3 from the Cauchy density f(x−θ), and discuss whether it has a finite first moment or not. Is there any unbiased estimator of θ for n = 3?