5. Consider an income distribution S: (5, 10, 20, 30, 50, 100). Suppose it is divided into two groups, group A: (5, 10, 30, 50) and group B: (20, 100). Let the poverty line be 60.

(i) Calculate the Poverty Gap and Squared Poverty Gap for distribution S.

(ii) Show that for both Head count and Poverty Gap, the weighted sum of poverty of groups A and B is the same as the overall poverty in S.