Suppose that a particle is released at the origin of the xy-plane and travels into the half-plane where x > O. Suppose that the particle travels in a straight line and that the angle between the positive half of the x-axis and this line is ex, which can be either positive or negative. Suppose, finally. that the angle ex has a uniform distribution on the interval (-Π/2Π/2). Let Y be the ordinate of the point at which the particle hits the vertical Hne x = 1. Show that the distribution of Y is a Cauchy distribution.