Suppose a gun sprays paint in a uniform back-and-forth movement, covering an angular sweep between forty five degrees to either side, onto a screen 100cm away. Assume that the distribution of paint at a distance ±x to either side of the centre of the screen is Cauchy, and that angular measure is computed in radians, distance in centimetres.
(a) What is the appropriate Cauchy density function for this distribution?
(b) What is the probability that paint will touch the screen more than 40cm to either side of the centre?