Let's consider two balanced dice. I am modelling each of them using

d1 = ProbabilityDistribution[1/6, {x, 1, 6, 1}]
d2 = ProbabilityDistribution[1/6, {x, 1, 6, 1}]

Call $x$ the result of the first dice and $y$ the result of the second dice after they are thrown, let $z=2x+y$. How can I make a probability distribution corresponding to $z$ using $d_1$ and $d_2$ ? I tried adding them


but this didn't work.

  • 2
    $\begingroup$ I think you want TransformedDistribution. $\endgroup$
    – Eric Brown
    Nov 26, 2015 at 18:57

1 Answer 1


As Eric Brown suggested you should use TransformedDistribution[]. Also I'd suggest using built in distributions if possible, here I mean DiscreteUniformDistribution[].

tf = TransformedDistribution[
  A + B, {A \[Distributed] DiscreteUniformDistribution[{1, 6}], 
   B \[Distributed] DiscreteUniformDistribution[{1, 6}]}]
PDF[tf, x]
DiscretePlot[PDF[tf, x], {x, 2, 12}]

enter image description here

  • 3
    $\begingroup$ Just as a tiny comment: it would be better to first evaluate: ee = PDF[tf, x], and then DiscretePlot[ee {x, 2, 12}] . By contrast, DiscretePlot[PDF[tf, x], {x, 2, 12}] might take about 100 times longer to plot, because it tells Mma to calculate PDF[t,x] at each value of x (rather than just solving it once). $\endgroup$
    – wolfies
    Nov 28, 2015 at 17:37

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