Suppose that a society has an income distribution of z={$'l, $3, $4, $7, $8} per day, where the income poverty line is z=$5. Calculate FGT index (indices) with inequality aversion parameter (alpha) is 0, 1 and 2. Using simple numerical examples of your own, verify if and when the FGT indices satisfies each of the following properties, known as "axioms" of poverty index: Monotonicity Axiom: a decrease in income of a poor person should increase the poverty index. Transfer Axiom: a transfer of income from poor to less poor should increase the poverty index. Transfer Sensitivity Axiom: the rise in the poverty index declines as the income transfer from poor to less poor is taken from richer poor