•Three Dice

The number of possibilities get bigger, but the idea is the same.  Now there are 6^3 = 216equally likely outcomes.  The smallest is 1+1+1=3 and the largest is 6+6+6=18.  We can let the computer generate the list.

In[41]:=

threeDice = Flatten[Table[i + j + k, {i, 6}, {j, 6}, {k, 6}]]

Out[41]=

{3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 1 ... 4, 10, 11, 12, 13, 14, 15, 11, 12, 13, 14, 15, 16, 12, 13, 14, 15, 16, 17, 13, 14, 15, 16, 17, 18}

In[42]:=

Histogram[threeDice]

[Graphics:../HTMLFiles/DiceStats_35.gif]

Out[42]=

-Graphics -

This histogram is starting to look like a bell curve - which is exactly what its heading towards.  

In[69]:=

μ3 = Mean[threeDice] // N

Out[69]=

10.5`

In[71]:=

σ3 = StandardDeviationMLE[threeDice] // N

Out[71]=

2.958039891549808`

In[75]:=

s3 = StandardDeviation[threeDice] // N

Out[75]=

2.9649110736105735`

Converted by Mathematica  (September 11, 2003)