1) Categorical variable tread Pattern = {A, B} and numerical variable tread Depth are used to classify Handling = {good, poor} of a vehicle. Depth is normally distributed with mean 9 and standard deviation 3 when Handling is good and mean 16 and standard deviation 4 when Handling is poor. There are 300 rows of data for training and the number of rows of data for each combination of Pattern and Handling are given in the table below.
Given row x_{0} = (Pattern = A, Depth=12). Use a naive Bayes' classifier to compute the class of Handling assigned to x_{0}. Show your work for full credit.