Science:Math Exam Resources/Courses/MATH103/April 2013/Question 06 (a)/Statement

Light Show on the Dance Floor

A laser is mounted 2m above the floor (see sketch) and its beam is directed along a straight line on the dance floor. For visual effects, the angle $\theta$ changes periodically and randomly. The angle $\theta$ is chosen uniformly in the interval $(-{\frac {\pi }{4}},{\frac {\pi }{4}})$, that is, the probability density function (pdf) is $p(\theta )={\frac {2}{\pi }}$ for $-{\frac {\pi }{4}}<\theta <{\frac {\pi }{4}}$ and zero elsewhere.

Find the cumulative distribution function (cdf), F(x) of the x-coordinate of the laser point on the floor.