  In the framework of the random matrix approach, we apply the theory of
Selberg's integral to problems of quantum transport in chaotic cavities. All
the moments of transmission eigenvalues are calculated analytically up to the
fourth order. As a result, we derive exact explicit expressions for the
skewness and kurtosis of the conductance and transmitted charge as well as for
the variance of the shot-noise power in chaotic cavities. The obtained results
are generally valid at arbitrary numbers of propagating channels in the two
attached leads. In the particular limit of large (and equal) channel numbers,
the shot-noise variance attends the universal value 1/(64\beta) that determines
a universal Gaussian statistics of shot-noise fluctuations in this case.
