申論題

12. (12%) A bunch of sensors are dropped from an aircraft to a forest for monitoring the oocu urrence of the wildfire. It is known that the wildfire can occur et random location (X, Y) in the forest with the joint PDF of X and Y as follows: It is found that dropped sensors are distributed over a square region with side length 2D centered at (0,0). Within the distribution region, the nurnber of sensors in any sub-region of area A follows the Poisson (ρA) distribution, where p is the distribution density (sensor/unit area). When a sensor is dropp opped to the gr malfunction that renders it totally useless. If a sensor is functiona, it has a circular detection ground, it has a probability q, 0 ＜ q ＜ l, of area πR² such that it can successfully detect the wildfire within a radius R with probability p, 0 ＜p ＜ 1, and not detect anything with probablity 1 -p. Assume for the typical scenario D＞R.