# Science:Math Exam Resources/Courses/MATH103/April 2013/Question 06 (b)

MATH103 April 2013
Other MATH103 Exams

### Question 06 (b)

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 ${\displaystyle \theta }$ changes periodically and randomly. The angle ${\displaystyle \theta }$ is chosen uniformly in the interval ${\displaystyle (-{\frac {\pi }{4}},{\frac {\pi }{4}})}$, that is, the probability density function (pdf) is ${\displaystyle p(\theta )={\frac {2}{\pi }}}$ for ${\displaystyle -{\frac {\pi }{4}}<\theta <{\frac {\pi }{4}}}$ and zero elsewhere.

Find the probability density function (pdf) for ${\displaystyle \displaystyle p(x)}$ of the x-coordinate of the laser point on the floor.

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