Suppose you are given $6$ training points as seen below, for a classification problem with two

binary attributes $x_1$ and $x_2$ and three classes Yin$\{1,2,3\}.$ You will use a decision tree learner

based on information gain.

$(1)$ Calculate the conditional entropy for both $x_1$ and $x_2.$

$(2)$ Calculate the information gain if we split based on $1)x_1$ or $2)x_2.$

$(3)$ Report which attribute is used for the first split. Draw the decision tree using this split.

$(4)$ Conduct classification for the test example $x_1=0$ and $x_2=1.$