Exercise $1.$ Consider the training examples shown below for a binary classification problem.

$\backslash$table$[[$Customer ID$,$Gender,Car Type,Shirt Size,Class$],[1,$M$,$Family,Small,C$0],[2,$M$,$Sports,Medium,C$0],[3,$M$,$Sports,Medium,C$0],[4,$M$,$Sports,Large,C$0],[5,$M$,$Sports,Extra Large,C$0],[6,$M$,$Sports,Extra Large,C$0],[7,$F$,$Sports,Small,C$0],[8,$F$,$Sports,Small,C$0],[9,$F$,$Sports,Medium,C$0],[10,$F$,$Luxury,Large,C$0],[11,$M$,$Family,Large,C$1],[12,$M$,$Family,Extra Large,C$1],[13,$M$,$Family,Medium,C$1],[14,$M$,$Luxury,Extra Large,C$1],[15,$F$,$Luxury,Small,C$1],[16,$F$,$Luxury,Small,C$1],[17,$F$,$Luxury,Medium,C$1],[18,$F$,$Luxury,Medium,C$1],[19,$F$,$Luxury,Medium,C$1],[20,$F$,$Luxury,Large,C$1]]$

$($a$)$ Compute the Gini index for the Gender attribute.

$($b$)$ Compute the Gini index for the Car Type attribute.

$($c$)$ Compute the Gini index for the shirt size attribute.

$($d$)$ Which of the above three attributes is better?