Simulate a binary classification dataset with a single feature via a mixture of normal distributions using R (Hint: Generate two data frames with the random number and a class label, and combine them together). The normal distribution parameters (using the function rnorm) should be (5,2) and (-5,2) for the pair of samples - you can determine an appropriate number of samples. Induce a binary decision tree (using rpart), and obtain the threshold value for the feature in the first split. How does this value compare to the empirical distribution of the feature? How many nodes does this tree have? What is the entropy and Gini at each? Repeat with normal distributions of (1,2) and (-1,2). How many nodes does this tree have? Why? Prune this tree (using rpart.prune) with a complexity parameter of 0.1. Describe the resulting tree.