$(2$ points$)$ One thing we can do with this dataset is measure the 'diversity of names per year. There are two

measures of diversity we can use:

Shannon Diversity Index: The Shannon Diversity Index is given by

$H^{\text{'}}=-{\displaystyle \underset{i=1}{\overset{N}{}}}{p}_{i}ln(p_i)$

where $N$ is the number of names, $p_i$ is the proportion of the $i^{th}$ name, and $ln$ the natural logarithm.

The Shannon Diversity Index makes two important assumptions:

all names are sampled; and

the sample is random.

Simpson Diversity Index: The Simpson Diversity Index is given by

$={\displaystyle \underset{i=1}{\overset{N}{}}}{p}_i^2$

where, again, $N$ is the number of names, and $p_i$ is the proportion of the $i^{th}$ name.

Note that rare names would have a very low $p_i$ value, and so rare names will not greatly affect the value

of $.$

The Shannon Diversity Index is a measure of 'true diversity'. The larger the number, the greater the

diversity.

The Simpson Diversity Index is actually a probability. It is the probability $$ that if you choose two

babies born at random that they have the same name.

Given this information and the information included in the data set, which diversity index do you think is more appropriate for our data and why?