Simulate a Derived Distribution
Generate random data from a component mixture distribution, using RandomVariate.
dist = MixtureDistribution[{2, 4 / 3}, {NormalDistribution[], NormalDistribution[2, 1 / 2]}];
SeedRandom[0];data = RandomVariate[dist, 10 ^ 4];Show[Histogram[data, 20, "ProbabilityDensity", ChartStyle -> "AlpineColors"], Plot[PDF[dist, x], {x, -9, 9}, PlotStyle -> {Thick, Blend[{Black, Red}]}], ImageSize -> 470]