  In a quantum system in a pure state, a subsystem generally has a nonzero
entropy because of entanglement with the rest of the system. Is the average
entanglement entropy of pure states also the typical entropy of the subsystem?
We present a method to compute the exact formula of the momenta of the
probability $P(S_A) \mathrm{d}S_A$ that a subsystem has entanglement entropy
$S_A$. The method applies to subsystems defined by a subalgebra of observables
with a center. In the case of a trivial center, we reobtain the well-known
result for the average entropy and the formula for the variance. In the
presence of a nontrivial center, the Hilbert space does not have a tensor
product structure and the well-known formula does not apply. We present the
exact formula for the average entanglement entropy and its variance in the
presence of a center. We show that for large systems the variance is small,
$\Delta S_A/\langle{S_{A}}\rangle\ll 1$, and therefore the average entanglement
entropy is typical. We compare exact and numerical results for the probability
distribution and comment on the relation to previous results on concentration
of measure bounds. We discuss the application to physical systems where a
center arises. In particular, for a system of noninteracting spins in a
magnetic field and for a free quantum field, we show how the thermal entropy
arises as the typical entanglement entropy of energy eigenstates.
