  The dispersion of a point set in $[0,1]^d$ is the volume of the largest axis
parallel box inside the unit cube that does not intersect with the point set.
We study the expected dispersion with respect to a random set of $n$ points
determined by an i.i.d. sequence of uniformly distributed random variables.
Depending on the number of points $n$ and the dimension $d$ we provide an upper
and lower bound of the expected dispersion. In particular, we show that the
minimal number of points required to achieve an expected dispersion less than
$\varepsilon\in(0,1)$ depends linearly on the dimension $d$.
