  We point out that the transmission eigenvalue density and higher order
correlation functions in chaotic cavities for an arbitrary number of incoming
and outgoing leads $(N_1,N_2)$ are analytically known from the Jacobi ensemble
of Random Matrix Theory. Using this result and a simple linear statistic, we
give an exact and non-perturbative expression for moments of the form
$<\lambda_1^m>$ for $m>-|N_1-N_2|-1$ and $\beta=2$, thus improving the existing
results in the literature. Secondly, we offer an independent derivation of the
average density and higher order correlation functions for $\beta=2,4$ which
does not make use of the orthogonal polynomials technique. This result may be
relevant for an efficient numerical implementation avoiding determinants.
