  We derive the joint distribution of the moments $\mathrm{Tr}\, Q^{\kappa}$
($\kappa\geq0$) of the Wigner-Smith matrix for a chaotic cavity supporting a
large number of scattering channels $n$. This distribution turns out to be
asymptotically Gaussian, and we compute explicitly averages and covariances.
The results are in a compact form and have been verified numerically. The
general methodology of proof and computations has a wide range of applications.
