A researcher wants to determine a procedure for discriminating between two multivariate populations. The researcher has enough data available to estimate the density functions f1(x) and f2(x) associated with populations π1 and π2, respectively. Let c(2|1) = 50 (this is the cost of assigning items as π2, given that π1 is true) and c(1|2) = 100. In addition, it is known that about 20% of all possible items (for which the measurements x can be recorded) belong to π2.
(a) Give the minimum ECM rule (in general form) for assigning a new item to one of the two populations.
(b) Measurements recorded on a new item yield the density values f1(x) = 3 and f2(x) = .5. Given the preceding information, assign this item to population π1 or population π2.