Suppose that a decision tree is trained on $1000$ training examples, and achieves $90\%$

accuracy on the training examples. What is the smallest and largest accuracy that this decision tree

can possibly achieve on a test set of $1000$ examples? Justify your answer. You can assume there are

only two classes.

$1$b $(20$ points$).$ Suppose that a decision tree is trained on $1000$ training examples, and achieves

$80\%$ accuracy on the training examples. What is the smallest and largest possible value for the

entropy at a leaf node of this decision tree? Remember that entropy is measured on the training set.

You can assume there are only two classes.

$1$c $(20$ points$).$ Suppose that a decision tree is trained on $1000$ training examples, and achieves

$100\%$ accuracy on the training examples. What is the smallest and largest possible value for the

entropy at a leaf node of this decision tree? Again, remember that entropy is measured on the

training set. You can assume there are only two classes.