Problem $2.$

Consider the following source of $($attribute$-$value, class$)$ pairs.

$(29,C2)(31,C2),(32,C1)(32,C1),(32,C2),(34,C2),(35,C2),(35,C2),(38,C2),(47,C2)$

$($a$)$ Find the source entropy.

$($b$)$ Compute the information gain for a threshold value $T=27.$

$($C$)$ Find the optimum threshold to separate the two classes, i$.$e$.,$ the threshold that maximizes the

information gain.