3 (Cost-sensitive classification). Suppose you face a binary classification prob- lem with input space X = R and output space Y = {0, 1}, where it is c times as bad to commit a \"false positive\" as it is to commit a \"false negative\" (for some real number c 1). To make this concrete, let's say that if your classifier predicts 1 but the correct label is 0, you incur a penalty of $c; if your classifier predicts 0 but the correct label is 1, you incur a penalty of 1. (And you incur no penalty if your classifier predicts the correct label.) Assume the distribution you care about N(0, class prior 0, and = 2/3 and 1/3, and the class conditional densities are has a1) for class with 0 N(1, 1/4) for1 = class 1. Let f * : R {0, 1} be the classifier with the smallest expected penalty. (a) (b) Assume 1 c 1.5. Specify precisely (and with a simple expression involving c) the region in which the classifier f * predicts 1. Now instead assume c 10. Specify precisely the region in which the classifier f predicts 1. 1 *