# 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.

• Please, when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! Commented Dec 21, 2014 at 23:27

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
Commented Dec 21, 2014 at 23:14
• @Jim Sorry, I don't understand what you mean by "w is distributed by 3" Commented Dec 21, 2014 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]]