•TwoDice

The sum of two dice can be anwhere from 2 to 12.  Since there are 6 ways the first dice can come up, and 6 ways for the second, there are 36 equally likely outcomes.  They are

In[26]:=

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

Out[26]=

{2, 3, 4, 5, 6, 7, 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, 12}

In[27]:=

Histogram[twoDice]

[Graphics:../HTMLFiles/DiceStats_20.gif]

Out[27]=

-Graphics -

In[35]:=

Histogram[BinCounts[twoDice, {1.5, 12.5, 1}], FrequencyData -> True]

[Graphics:../HTMLFiles/DiceStats_23.gif]

Out[35]=

-Graphics -

In[63]:=

μ2 = Mean[twoDice] // N

Out[63]=

7.`

In[67]:=

σ2 = StandardDeviationMLE[twoDice] // N

Out[67]=

2.41522945769824`

In[68]:=

s2 = StandardDeviation[twoDice] // N

Out[68]=

2.449489742783178`

Converted by Mathematica  (September 11, 2003)