The overlapping area of the two probability density functions of Figure 11.1 represents the region in which there is the potential for false positives and false negatives. Further, Figure 11.1 is an...

The overlapping area of the two probability density functions of Figure 11.1 represents the region in which there is the potential for false positives and false negatives. Further, Figure 11.1 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. Observe, that the overlap region equally covers authorized users and intruders. Does it always mean there is equal probability that events in this region are by authorized users and intruders? Justify your answer.