Question: Suppose that we will learn a decision tree to predict if students pass a class (Y or N) using the dataset below, based on their

Suppose that we will learn a decision tree to predict if students pass a class (Y or N) using the dataset below, based on their current GPA (H, M, or L) and whether or not they studied (S or NS). Use log2, i.e., the log base is 2, when you calculate and write answers. Show the steps how you obtain the result for all questions below for full credits.

What is the entropy of the attribute "Passed"?

If we were to split using the attribute "GPA", (a) what are the entropies of each of the three children nodes (i.e., GPA=L, GPA=M, and GPA=H) and (b) what is the weighted entropy of the three children nodes from the split?

If we were to split using the attribute "Studied", (a) what are the entropies of each of the two children nodes (Studied=S and Studied=NS) and (b) what is the weighted entropy of the two children nodes from the split?

(4) Which attribute should be split first? Explain why.

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