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.
I don't know what to tell you, that's exactly how the problem was given.
Right, I understand X = n sec(t) , I think it's the fact that you have a uniform distribution so you have 1/(b-a) as being the area.
Then you can use the fact that X = n sec(t) to find the upper limit on the integral (since the cdf would be the integral and the density function is its derivative).