I would like to simulate from a joint distribution multiplied by a constant.

e.g. 3*NormalDistribution[0,1]*NormalDistribution[1,1]

I tried using something like ProductDistribution but that doesn't work.

Can anyone give me any hints.


1 Answer 1



d1 = NormalDistribution[];
d2 = NormalDistribution[1, 1];
d3 = TransformedDistribution[3 x y, {Distributed[x, d1], Distributed[y, d2]}];
(* or d3 = TransformedDistribution[3 x y, 
   Distributed[{x, y}, BinormalDistribution[{0, 1}, {1, 1}, 0]]]; thanks: @BobHanlon *)

data = RandomVariate[d3, 100];
Histogram[data, 10, "PDF"]

enter image description here

  • 1
    $\begingroup$ d3 can also be defined as d3 = TransformedDistribution[3*x*y, Distributed[{x, y}, BinormalDistribution[{0, 1}, {1, 1}, 0]]]; This form is more general and could readily handle cases where x and y are correlated. $\endgroup$
    – Bob Hanlon
    Commented Dec 19, 2014 at 5:17

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