e. Compute the Gini index for the cases $$ L(x)=x^{p} $$ and $$ p=1.1,1,3,2,3,4 $$. The Gini index for $$ p=1.1 $$ is 0.048 . (Type an integer or decimal rounded to three decimal places as needed.) The Gini index for $$ p=1.3 $$ is 0.13 . (Type an integer or decimal rounded to three decimal places as needed.) The Gini index for $$ p=2 $$ is 0.333 . (Type an integer or decimal rounded to three decimal places as needed.) The Gini index for $$ p=3 $$ is 0.5 . (Type an integer or decimal rounded to three decimal places as needed.) The Gini index for $$ p=4 $$ is $$ \square $$. (Type an integer or decimal rounded to three decimal places as needed.)

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To compute the Gini index for $$ L(x) = x^p $$, we use the following formula:

$$
\text{Gini Index} = 1 - \frac{2}{p + 1}
$$

Let's apply this formula for $$ p = 4 $$:

$$
\text{Gini Index} = 1 - \frac{2}{4 + 1} = 1 - \frac{2}{5} = 1 - 0.4 = 0.6
$$

Rounded to three decimal places, the Gini index for $$ p = 4 $$ is:

$$
0.600
$$

**Answer:**  
0.600
The Gini index for $$ p=4 $$ is 0.600.

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