Let l n denote the line x = n in the Cartesian plane.

l n = {(n,t) : t E R}

A laser is positioned at the point (0,0). Suppose that the laser points into the first quadrant uniformly. Let X be the distance between (0,0) and the point that the laser hit on the line l n.

a) Find an explicit formula for the cumulative distribution function Fx (t) of X.

b) Find an explicit formula for the density function fx(t) of X.