Mild $1.(10$ points$)$ Given the following dataset, use Decision Tree algorithm to classify the data: Day Outlook Temperature Humidity Play Tennis $1$ Sunny Hot High No Sunny Mild High No Rain Cool High No Rain High No $5$ Sunny Hot Normal Yes $6$ Overcast Hot Normal Yes $7$ Overcast Mild Normal Yes $8$ Overcast Cool High Yes $9$ Rain Cool Normal Yes $10$ Rain Mild Normal Yes a$.$ What is the entropy of this dataset with respect to the target feature $($play tennis$)?$ Show calculation details. b$.$ What is the information gain of Humidity relative to this dataset? What is its SplitInfo and gain ratio? c$.$ What's the gini reduction of Outlook feature relative to the dataset? d$.$ For the dataset in problem $1,$ if a new instance is $($outlook $=$ sunny, temperature $=$ mild, humidity $=$ normal$),$ based on Na$$ve Bayesian Learning, how will the new instance be classified? Please use Laplace smoothing if any conditional probability is zero. Show all calculation details