Truncate a Distribution
The PDF of TruncatedDistribution is more peaked and is nonzero on a smaller domain when compared with the original distribution.
LeftTruncated𝒟 = TruncatedDistribution[{-1, ∞}, NormalDistribution[]];
RightTruncated𝒟 = TruncatedDistribution[{-∞, 1}, NormalDistribution[]];
DoubleTruncated𝒟 = TruncatedDistribution[{-1, 1}, NormalDistribution[]];g1 = Table[Plot[{PDF[m, x], PDF[NormalDistribution[], x]}, {x, -3, 3}, Filling -> Axis, Exclusions -> None], {m, {LeftTruncated𝒟, RightTruncated𝒟, DoubleTruncated𝒟}}];𝒟 = ProductDistribution[NormalDistribution[], LaplaceDistribution[-1 / 2, 1]];𝒯1 = TruncatedDistribution[{{-∞, 1}, {-∞, ∞}}, 𝒟];
𝒯2 = TruncatedDistribution[{{-∞, ∞}, {-∞, 1}}, 𝒟];𝒯3 = TruncatedDistribution[{{-∞, 1}, {-∞, 1}}, 𝒟];g2 = Table[Plot3D[Evaluate[{PDF[𝒟, {x, y}], PDF[m, {x, y}]}], {x, -2, 2}, {y, -2, 2}, PlotTheme -> "Classic", PlotStyle -> {Lighter@ColorData[1, 1], Directive[Lighter@ColorData[1, 2], Opacity[0.7]]}, PlotRange -> All, Lighting -> "Neutral", ExclusionsStyle -> Directive[Yellow, Opacity[0.5]], Mesh -> None, AxesLabel -> Automatic], {m, {𝒯1, 𝒯1, 𝒯3}}];GraphicsGrid[{g1, g2}, ImageSize -> 550, Spacings -> {Automatic, 150}]