(b) An economist decides to model the distribution of income in a country with the probability density function: aka fx (x; o, k) = for e > k and 0 otherwise, where k > 0 and o > 2. Let {X1, X2, ..., Xn} be a random sample of size n from this distribution. You may use the fact that: ak ock2 E(X) = and E(X] ) = a - 1 a - 2 Show that the method of moments estimators of o and & are the solutions of: 1 n - 1 (a - 1)X a(c - 2) X2 and k = where: X = 1 X; and S* = E(xi - X)?. n 1=1 n - 1 i=1