Suppose you observe a random sample x1,x2,..., X of ages from a Cauchy distribution with median θ and known scale parameters, that is, f(xi) = 1/1 + (xi - θ^2)/s^2, suppose s = 5 and the dataset of ages is given below 27, 24, 33, 33, 29, 36, 28, 27, 31, 26, 30, 41, 23, 29, 34, 38, 36, 29, 26, 24 We are interested in finding the maximum likelihood estimation (MLE) of θ. Complete the following steps for your answer. (iii) Plot the likelihood function on a fine grid of θ values. (iv) Estimate the MLE of θ using the Newton-Raphson optimization methods.