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Problem 1. The Cauchy distribution with scale 1 has following density function f(x) = 1 /...

Problem 1. The Cauchy distribution with scale 1 has following density function
f(x) = 1 / π [1 + (x − η)^2 ] , −∞ < x < ∞.
Here η is the location and rate parameter. The goal is to find the maximum likelihood estimator of η.

(a) Find the log-likelihood function of f(x)

l(η; x1, x2, ..., xn) = log L(η; x1, x2, ..., xn) =

(b) Find the first derivative of the log-likelihood function

l'(η; x1, x2, ..., xn) =

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