Question: Consider a random sample of size n from a Pareto distribution, Xi ~ PAR (theta, 2).

(a) Find the ML Equation d/d theta (ln L(theta)) = 0

(b) From the data of Example 4.6.2, compute the ML estimate, theta hat, to three decimal places. Note: the ML equation cannot be solved explicitly for theta hat, but it can be solved numerically, by an iterative method, or by trial and error.

Data: xi: 0.85, 1.08, 0.35, 3.28 1.24 2.58 0.02 0.13 0.22 0.52

yi: 0.02, 0.13, 0.22, 0.35, 0.52, 0.85, 1.08, 1.24 2.58, 3.28