There are four descriptive features and one target feature in this dataset, as follows:

$$AGE$,$ a continuous feature listing the age of the individual;

$$EDUCATION$,$ a categorical feature listing the highest education award achieved by the individual $($high school, bachelors, doctorate$)$;

$$MARITAL STATUS $($never married, married, divorced$)$;

$$OCCUPATION $($transport $=$ works in the transportation industry; professional $=$ doctor, lawyer, or similar; agriculture $=$ works in the agricultural industry; armed forces $=$ is a member of the armed forces$)$; and

$$ANNUAL INCOME, the target feature with $3$ levels $($a$25$K$,25$K$50$K$,$ a$50$K$).($a$)$ Calculatetheentropyforthisdataset.

$($b$)$CalculatetheGiniindexforthisdataset$.$

$($c$)$In building a decision tree, the easiest way to handle a continuous feature is to define a threshold around which splits will be made. What would be the opti$-$ mal threshold to split the continuous AGE feature $($use information gain based on entropy as the feature selection measure$)?$

$($d$)$Calculate information gain $($based on entropy$)$ for the EDUCATION, MARITAL STATUS, and OCCUPATION features.

$($e$)$Calculatetheinformationgainratio$($basedonentropy$)$forEDUCATION$,$MAR$-$ ITAL STATUS, and OCCUPATION features.

$($f$)$CalculateinformationgainusingtheGiniindexfortheEDUCATION$,$MARITAL STATUS, and OCCUPATION features.