  In the hot electron regime, electron-electron scattering strongly modifies
not only the shot noise but also the full counting statistics. We employ a
method based on a stochastic path integral to calculate the counting statistics
of two systems in which noise in the hot electron regime has been
experimentally measured. We give an analytical expression for the counting
statistics of a chaotic cavity and find that heating due to electron-electron
scattering renders the distribution of transmitted charge symmetric in the shot
noise limit. We also discuss the frequency dispersion of the third order
correlation function and present numerical calculations for the statistics of
diffusive wires in the hot electron regime.
