Question $1$:

$\backslash$table$[[$Temperature$,$Humidity,PlayTennis$],[$Hot$,$High,No$],[$Hot$,$Normal,Yes$],[$Mild$,$High,No$],[$Mild$,$Normal,Yes$],[$Cold$,$High,Yes$],[$Cold$,$Normal,Yes$]]$

For this problem, you can write your answers using $lo{g}_2,$ but it may be helpful to note that $lo{g}_{2}3$~~ $1\mathrm{.}6.$

i$)$ What is the initial entropy of the training sample?

ii$)$ What is the information gain for $($PlayTennis $|$ Temperature$)?$

iii$)$ What is the entropy and gain for $($PlayTennis $|$ Humidity$)?$

iv$)$ Draw the full decision tree that would be learned for this dataset. You do not need to show any calculations.

Question $2$:

A dataset has been collected to develop a classifier. It requires the following information to understand its features. Do this exercise for the dataset that you have selected for your own project.

Number of Classes

Number of Features $($Variables$)($how many of them are categorical and how many of them are continuous$)$

Number of Samples

Number of Samples for each class

How imbalance the dataset is

Average value of each feature $($variable$)$ and its standard deviation for each class

Normalise the data according the maximum and the difference between maximum and minimum values for each feature, and discuss how it may affect the classifier design.