2. Consider the decision problem of whether a student should choose to eat Pizza, Burger or Salad depending on whether it is for lunch or dinner. We conduct a survey on 100 students and ask them what they would choose to eat (Y) if it is for lunch or dinner (X). The responses are as follows: (a) What is the entropy of choosing what to eat, H(Y) ? (b) What is the entropy of choosing what to eat, given the knowledge of whether it is for lunch or for dinner, H(YX) ? (c) What is the information gain about choosing what to eat if we have the knowledge of whether it is for lunch or for dinner, IG(YX) ? (d) Suppose that there is another feature (W) that describes whether the day is a weekday or a weekend. Assume that in our decision tree, we always split the tree based on weekday/weekend first instead of lunch/dinner. What is the range of values of IG(YW) for this decision tree