1) The area that individual paint droplets will cover on a surface is being investigated to attempt

to improve paint spraying efficiency at a certain automobile manufacturing plant. Suppose

that, using a particular sprayer, the area covered by a paint droplet is random and exponentially

distributed with parameter = 50 mm2. If the paint coverage areas are circular,

a) derive the exact distribution of the radius of the coverage areas, and,

b) use this to determine the probability that a paint droplet will have a coverage with

radius in excess of 0.1 mm.