Dice problem

• To: mathgroup at smc.vnet.net
• Subject: [mg81281] Dice problem
• From: "AngleWyrm" <anglewyrm at yahoo.com>
• Date: Tue, 18 Sep 2007 00:44:32 -0400 (EDT)

```With a set of three six-sided dice, display the chance-weights and
probabilities of each outcome:

numSides=6; numDice=3;
poly = Sum[x^i, {i, numSides}]^numDice // Expand;
c = CoefficientList[poly, x];
Table[{x, c[[x + 1]], c[[x + 1]]/Total[c] // N}, {x, numDice,
numDice numSides}] // TableForm

So far, so good. Next, I want to model this discrete distribution with a
continuous distribution. That is to say, I want a continuous distribution
that produces the same probabilities at these sixteen points (3..18). My
first attempt was to take the Mean and StandardDeviation of my coefficients
list, and attempt to generate a gaussian distribution on it like so:

test = RandomReal[ NormalDistribution[Mean[c], StandardDeviation[c]], 1000];
ListPlot[test]
{Min[test], Max[test]} // N

But the result produces a much larger range of outcomes, approximately {-25,
45}. Any set generated on this larger range will have smaller probabilities
for the target range of 3..18.

Is there some method or model to reduce the error between the mathematical
model and the dataset?

```

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