  The statistical properties of quantum transport through a chaotic cavity are
encoded in the traces $\T={\rm Tr}(tt^\dag)^n$, where $t$ is the transmission
matrix. Within the Random Matrix Theory approach, these traces are random
variables whose probability distribution depends on the symmetries of the
system. For the case of broken time-reversal symmetry, we present explicit
closed expressions for the average value and for the variance of $\T$ for all
$n$. In particular, this provides the charge cumulants $\Q$ of all orders. We
also compute the moments $<g^n>$ of the conductance $g=\mathcal{T}_1$. All the
results obtained are exact, {\it i.e.} they are valid for arbitrary numbers of
open channels.
