Population of a phononic mode coupled to a single-electron transistor in the sequential tunneling regime is discussed for the experimentally realistic case of intermediate electron-phonon coupling. Features like a sub-Poissonian bosonic distribution
are found in regimes where electron transport drives the oscillator strongly out of equilibrium with only few phonon states selectively populated. The electron Fano factor is compared to fluctuations in the phonon distribution, showing that all possible combinations of sub- and super-Poissonian character can be realized.
