Mr. Hood is a good archer. He can regularly hit a target having a 3- ft. diameter and often hits the bull’s- eye, which is 0.5 ft. in diameter, from 50 ft. away. Suppose the miss is measured as the radial distance from the center of the target and, furthermore, that the radial miss distance is a Rayleigh random variable with the constant in the Rayleigh PDF being σ2 = 4( sq- ft).
(a) Determine the probability of Mr. Hood’s hitting the target.
(b) Determine the probability of Mr. Hood’s hitting the bull’s- eye.
(c) Determine the probability of Mr. Hood’s hitting the bull’s- eye given that he hits the target.