Consider the test Ho : Y = N H1 : Y =S+N, where S ~ U[-1, 1] and N ~ U[-2, 2], and S, N are independent. (a) Set up the LRT and determine the decision regions when the threshold is (i) k = 1/4, (ii) k = 2 and (iii) k = 1. (b) Find PD and PFA for each of these thresholds. (c) Plot the ROC