Consider the table for a 2-class tree classifier with classes (+,-) below giving the number of +'s and 's reaching each node. node +/- 2 3 4 5 6 7 8 9 18 19 40/60 0 22/35 0 0 terminal 18/25 15/5 7/30 1 12/5 1 6/20 7/2 8/3 7/0 1/3 0 The nodes are numbered so that 1 is the root, while the children of node k are 2k and 2k +1. The "terminal" column says if a node is terminal or not. (a) (1 pt) Construct the tree as a graph (the usual depiction of a tree) labeling the nodes with numbers and giving the classification each node and the number of errors it would produce if it were a terminal node. You can draw the tree by hand (b) (1 pt) Compute R(T) where T is the tree given in the example and R(T) is our probabability of error for the tree when tested on the training set. (c) (1 pt) Explain why you do or do not believe this is an accurate representation of the tree's performance on new data. (d) (1 pt) Compute the optimal penalized risk, R for each node of T where a 03. Give the corresponding optimal tree Te. You can draw the tree by hand. hints: Work from terminal nodes, also consider the example discussed in the class. (e) (1 pt) How much do you need to increase a before a different To appears? Same question for decreasing a. hints: calculate a when R is equal R(T)