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the previous assignment, you leàrnéd åbóüt ini indéx öf à country (a number measuring the country's income inequality) is closely related to the area under the country's Lorenz curve over the interval (0, 1]. Let's recall that if the point (10 1ố0) is on the Lorentz curve, then this means that the bottom a% of households receive 6% of the country's total income. In reality, we do not have a formula for the Lorenz curve but a collection of data. The following is data of Canadian households' (disposable) income in 2020. (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3610058701) Let's focus on the following 6 data points on the Lorenz curve LCanada- 0 0.2 LCanada(x) | 0 0.068 | 0.201 | 0.378 | 0.607 | 1 0.4 0.6 0.8 1 So, for example, the point (0.2, 0.068) is on the Lorenz curve LCanada. This means that the bottom 20% of Canadian households received 6.8% of Canada's total (household disposable) income in 2020. (a) LCanada Over the interval (0, 1] by L5, the left endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (b) LCanada Over the interval (0, 1] by R5, the right endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (c) LCanada Over the interval (0, 1] by T3, the Trapezoidal Rule. Use the data points above to approximate the area under the Lorenz curve (d) determine if T; is an underestimate or an overestimates. It is known that Lorenz curves are always concave upward. Using this fact,

the previous assignment, you leàrnéd åbóüt ini indéx öf à country (a number measuring the country's income inequality) is closely related to the area under the country's Lorenz curve over the interval (0, 1]. Let's recall that if the point (10 1ố0) is on the Lorentz curve, then this means that the bottom a% of households receive 6% of the country's total income. In reality, we do not have a formula for the Lorenz curve but a collection of data. The following is data of Canadian households' (disposable) income in 2020. (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3610058701) Let's focus on the following 6 data points on the Lorenz curve LCanada- 0 0.2 LCanada(x) | 0 0.068 | 0.201 | 0.378 | 0.607 | 1 0.4 0.6 0.8 1 So, for example, the point (0.2, 0.068) is on the Lorenz curve LCanada. This means that the bottom 20% of Canadian households received 6.8% of Canada's total (household disposable) income in 2020. (a) LCanada Over the interval (0, 1] by L5, the left endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (b) LCanada Over the interval (0, 1] by R5, the right endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (c) LCanada Over the interval (0, 1] by T3, the Trapezoidal Rule. Use the data points above to approximate the area under the Lorenz curve (d) determine if T; is an underestimate or an overestimates. It is known that Lorenz curves are always concave upward. Using this fact,

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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4. In the previous assignment, you learned about the Gini index of a country number measuring the country's income inequality) is closely related to the area under the country's Lorenz curve over the interval [0, 1]. Let's recall that if the point (, 1Ố) is on the Lorentz curve, then this means that the bottom a% of households receive 6% of the country's total income. In reality, we do not have a formula for the Lorenz curve but a collection of data. The following is data of Canadian households' (disposable) income in 2020. (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3610058701) Let's focus on the following 6 data points on the Lorenz curve LCanada. 0 0.2 LCanada (2) 0 0.068 0.201 0.378 0.607 1 0.4 0.6 0.8 1 So, for example, the point (0.2, 0.068) is on the Lorenz curve LCanada: This means that the bottom 20% of Canadian households received 6.8% of Canada's total (household disposable) income in 2020. (a) LCanada over the interval [0, 1] by L5, the left endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (b) LCanada Over the interval [0, 1] by R5, the right endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (c) LCanada over the interval [0, 1] by T,, the Trapezoidal Rule. Use the data points above to approximate the area under the Lorenz curve (d) determine if T; is an underestimate or an overestimates. It is known that Lorenz curves are always concave upward. Using this fact,
Transcribed Image Text:4. In the previous assignment, you learned about the Gini index of a country number measuring the country's income inequality) is closely related to the area under the country's Lorenz curve over the interval [0, 1]. Let's recall that if the point (, 1Ố) is on the Lorentz curve, then this means that the bottom a% of households receive 6% of the country's total income. In reality, we do not have a formula for the Lorenz curve but a collection of data. The following is data of Canadian households' (disposable) income in 2020. (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3610058701) Let's focus on the following 6 data points on the Lorenz curve LCanada. 0 0.2 LCanada (2) 0 0.068 0.201 0.378 0.607 1 0.4 0.6 0.8 1 So, for example, the point (0.2, 0.068) is on the Lorenz curve LCanada: This means that the bottom 20% of Canadian households received 6.8% of Canada's total (household disposable) income in 2020. (a) LCanada over the interval [0, 1] by L5, the left endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (b) LCanada Over the interval [0, 1] by R5, the right endpoint approximation. Use the data points above to approximate the area under the Lorenz curve (c) LCanada over the interval [0, 1] by T,, the Trapezoidal Rule. Use the data points above to approximate the area under the Lorenz curve (d) determine if T; is an underestimate or an overestimates. It is known that Lorenz curves are always concave upward. Using this fact,
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