Problem 4 Consider a binary classication problem with l-dimensional feature space R with base distribution D over R X {0,1}. Suppose that the data generating process (prior to any strategic adaptation) takes the following form: X|Y=1~N(1,1) X|Y=0~N(0,1). In this problem, we examine properties of decision rules f : R > {0,1} in the presence of strategic adaptation. The loss function that we consider is (y, y') = 0 if y = y' and 1 otherwise. Assume that the cost function is of the form C(:L'1,IL'2) = |sc1 .1:2|; assume also that agents change their features according to the \"standard model\