  We study theoretically the full distribution of transferred charge in a
tunnel junction (or quantum point contact) coupled to a nanomechanical
oscillator, as well as the conditional evolution of the oscillator. Even if the
oscillator is very weakly coupled to the tunnel junction, it can strongly
affect the tunneling statistics and lead to a highly non-Gaussian distribution.
Conversely, given a particular measurement history of the current, the
oscillator energy distribution may be localized and highly non-thermal. We also
discuss non-Gaussian correlations between the oscillator motion and tunneling
electrons; these show that the tunneling back-action cannot be fully described
as an effective thermal bath coupled to the oscillator.
