# Random Variate from a transformed Distribution

I would like to simulate random variates from a transformed distribution of a joint distribution and a constant.

i.e.

joint=ProductDistribution[NormalDistribution[],BetaDistribution[1,2],BetaDistribution[2,2]];
transform=TransformedDistribution[3*joint....]


I am unsure how to complete the transformed distribution code to put in the variables.

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joint = ProductDistribution[NormalDistribution[], BetaDistribution[1, 2], BetaDistribution[2, 2]];
q = TransformedDistribution[{x, y, z} w, {{x, y, z} \[Distributed]  joint,
w \[Distributed] UniformDistribution[]}]
ListPlot3D@RandomVariate[joint, 100]


• Thanks for the help. Am I allowed to just say w is distributed by 3? I have an exact constant I would like to use. – Jim Dec 21 '14 at 23:14
• @Jim Sorry, I don't understand what you mean by "w is distributed by 3" – Dr. belisarius Dec 21 '14 at 23:26
joint = ProductDistribution[NormalDistribution[], BetaDistribution[1, 2], BetaDistribution[2, 2]];
td = TransformedDistribution[3 {x, y, z} , Distributed[{x, y, z}, joint]];

Through@{Mean, Variance}@td
(* {{0,1,3/2}, {9,1/2,9/20}} *)

PDF[td, {x, y, z}]


ListPlot3D[RandomVariate[td, 50]]