Question 2 only

The Gini index is a statistical measure of income distribution. It ranges from 0 (or 0%) for perfect equality to 1 (or 100%) for perfect inequality. Source: https://data.worldbank.org/indicator/SI.POV.GINI?view=map . A country where every 1. Perfect Equality 2. Unequal 3. More Unequal 4. Total Inequality resident has the same 100%% . . . . . . . . . .. .. . . . . . . ... ... . . . . . . . . . .. income would have a Gini index of 0. G1=0 G3> G2 A country in which one G4=1 resident earned all the Population income, while everyone else earned nothing, would have a Gini index of 1. multiply find shaded aven then by 2 The Gini index is defined to be two times the area between the line of perfect equality (y = x) and the Lorenz curve. (The Lorenz Curve - Ukraine 2020 Lorenz curve shows the percentage of income held by each y = 1.5625x5 - 2.5781x* + 1.3438x3 percentile of the country's population. As an example, the + 0.2406x3+ 0. 4313x Lorenz curve would plot a point at (50, 20) if the bottom 50% 0.8 Ukraine -Line of Equality of the population held 20% of the country's income.) 3 0 . Talks were underway for Ukraine to join the European Union Cumulative V an alliance which currently includes the countries of Austria, 0.2 Belgium, Bulgaria, Croatia, Cyprus, Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, 0.2 0.4 0.6 0.8 Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Cumulative Percentage of the Population Portugal, Romania, Slovakia, Slovenia, Spain and Sweden. We are going to compare the income distribution of Ukraine with that of Poland, a country in the EU which is geographically close to Ukraine. 1. Above is a plot of the line of equality and the Lorenz curve for Ukraine in 2020. Shade the area we need to find first so that we can calculate the Gini index. Then, write an expression for THIS AREA that includes a definite integral. Area of Aminus area under Lorenz curve 1/ 2 - S ( 1 . 56 2 5 x 5 - 2 578 1 x 4 + 1 343 8 * 3 + 0 . 240 6 * 2 + 0 , 4313 * ) olx Evaluate T then x 2 2. Use the integral expression you wrote in #1 and the Fundamental Theorem of Calculus to find the Gini index for Ukraine in the year 2020. Show the substitutions necessary, but use fnint to do the calculation