The overlapping area of the two probability density functions of Figure 19.6 represents the region in which there is the potential for false positives and false negatives. Further, Figure 19.6 is an idealized and not necessarily representative depiction of the relative shapes of the two density functions. Suppose there is 1 actual intrusion for every 1000 authorized users, and the overlapping area covers 1% of the authorized users and 50% of the intruders.
a. Sketch such a set of density functions and argue that this is not an unreasonable depiction.
b. What is the probability that an event that occurs in this region is that of an authorized user? Keep in mind that 50% of all intrusions fall in this region.