Full counting statistics of a charge pump in the Coulomb blockade regime

We study full charge counting statistics (FCCS) of a charge pump based on a nearly open single electron transistor. The problem is mapped onto an exactly soluble problem of a nonequilibrium $g=1/2$ Luttinger liquid with an impurity. We obtain an analytic expression for the generating function of the transmitted charge for an arbitrary pumping strength. Although this model contains fractionally charged excitations only integer transmitted charges can be observed. In the weak pumping limit FCCS correspond to a Poissonian transmission of particles with charge ${e}^{*}=e/2$ from which all events with odd numbers of transferred particles are excluded.