Apply censoring to a distribution

LeftCensored𝒟 = CensoredDistribution[{5, ∞}, PoissonDistribution[7]];
RightCensored𝒟 = CensoredDistribution[{-∞, 9}, PoissonDistribution[7]];
DoubleCensored𝒟 = CensoredDistribution[{5, 9}, PoissonDistribution[7]];g1 = Table[DiscretePlot[{PDF[m, x], PDF[PoissonDistribution[7], x]}, {x, 0, 13}, ExtentSize -> 0.5], {m, {LeftCensored𝒟, RightCensored𝒟, DoubleCensored𝒟}}];

LeftCensored𝒟 = CensoredDistribution[{-1, ∞}, NormalDistribution[]];
RightCensored𝒟 = CensoredDistribution[{-∞, 1}, NormalDistribution[]];
DoubleCensored𝒟 = CensoredDistribution[{-1, 1}, NormalDistribution[]];g2 = Table[Plot[{CDF[m, x], CDF[NormalDistribution[], x]}, {x, -3, 3}, Filling -> Axis, Exclusions -> None], {m, {LeftCensored𝒟, RightCensored𝒟, DoubleCensored𝒟}}];

GraphicsGrid[{g1, g2}, ImageSize -> {550, 330}, Spacings -> {Automatic, 170}]

-Graphics-