The na$$ve Bayes method is an ensemble method, as we learned in Lecture $5.$ Assume we have three classifiers, and their predicted results are given in Table $4\mathrm{.}1.$ The confusion matrix of each classifier is given in Table $4\mathrm{.}2.$ Calculate the final decision using the Na$$ve Bayes method: Table $4\mathrm{.}1$ Sample x Result Classifier $1$ Class $1$ Classifier $2$ Class $1$ Classifier $3$ Class $2$ Table $4\mathrm{.}2$ Programming Problem$($s$)$: $5.$ Use decision tree and random forest to train models using the titanic.csv dataset included in this assignment. Step $1$: Read titanic.csv and observe a few samples, noting that there are both categorical and numerical features. If some features are missing, fill them in using the average of the same feature of other samples. Take a random $80\%$ of samples for training and use the remaining $20\%$ for testing. Step $2$: Fit a decision tree model using independent variables $$pclass $+$ sex $+$ age $+$ sibsp$$ and dependent variable $$survived$.$ Plot the full tree. Make sure $$survived$$ is a qualitative variable taking $1($yes$)$ or $0($no$)$ in your code. You may see a tree similar to this one, but the actual structure and size may vary: Step $3$: Use the GridSearchCV$()$ function to find the best value for the parameter max$\_$leaf$\_$nodes to prune the tree. Plot the pruned tree, which will be smaller than the tree you obtained in Step $2.$ b$)$ Classifier $1$ Class $1$ Class $2$ Class $14010$ Class $23020$ a$)$ Classifier $2$ Class $1$ Class $2$ Class $12030$ Class $22030$ c$)$ Classifier $3$ Class $1$ Class $2$ Class $1500$ Class $24010$