Q3 (5+10+5+15=35 points) Suppose you observe a random sample X1.X2.... Xn of ages from a Cauchy distribution with median θ and known scale parameter s, that is
f(x¹) = 1 / 1 + (x¹ - θ)²/s²
Supposes 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.
(i) read the data into R.
(ii) create a function in R to compute the log-likelihood.