  For the Vlasov-Poisson-Boltzmann equations with random uncertainties from the
initial data or collision kernels, we proved the sensitivity analysis and
energy estimates uniformly with respect to the Knudsen number in the diffusive
scaling using hypocoercivity method. As a consequence, we also justified the
incompressible Navier-Stokes-Poisson limit with random inputs. In particular,
for the first time, we obtain the precise convergence rate {\em without}
employing any results based on Hilbert expansion. We not only generalized the
previous deterministic Navier-Stokes-Poisson limits to random initial data
case, also improve the previous uncertainty quantification results to the case
where the initial data include both kinetic and fluid parts.
