Question

The density function for the number of times the riders scream on a roller coaster is given by f(x). Find the mean number of screams over the course of the ride.

Answer 1

The mean is given by

$\mathbb E(X)=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac1{4\pi}\int_0^{4\pi}x(1-\cos 6x)\,\mathrm dx=2\pi$

Answer 2

Check answer above this one :)