Problem 3. The Lorenz curve y income distribution in a given country. By definition, L(r) is the fraction of the total income that goes to the bottom rth part of the population, where 0
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![Problem 3. The Lorenz curve y
income distribution in a given coUntry. By definition, L(r) is the fraction
of the total income that goes to the bottom rth part of the population, where
0<r<1. For example, if F(0.4) = 0.245, then the bottom 40% of households
receive 24.5% of the total income. If A is the area between y = r and y = F(r)
and B is the area under y =r over [0, 1], then Gini inder is defined by
L(r) is used by economists to study
A
2| (r – L(r)) dr.
B
Calculate the Gini inder of the United States in the year 2001 from the Lorenz
curve in Figure 22, which consists of segments joining the data points in the
following table:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9983f52a-edb7-45ac-9eba-18f4f4f10772%2F478f4d32-dc93-4e95-8de5-893231e5b8c7%2F5tf1twj_processed.png&w=3840&q=75)
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