•Eight Dice

Way too big to do by hand, but we can still (barely) have the computer do the whole population for us.

In[117]:=

dice = 0 ; Do[dice = Table[i + dice, {i, 1, 6}], {8}] ; dice = Flatten[dice] ;

In[123]:=

diceFreq = BinCounts[dice, {6, 48, 1}]

Out[123]=

{0, 1, 8, 36, 120, 330, 792, 1708, 3368, 6147, 10480, 16808, 25488, 36688, 50288, 65808, 82384 ... 98813, 82384, 65808, 50288, 36688, 25488, 16808, 10480, 6147, 3368, 1708, 792, 330, 120, 36, 8, 1}

Now there's a true Normal distribution.

In[124]:=

Histogram[diceFreq, FrequencyData -> True]

[Graphics:../HTMLFiles/DiceStats_47.gif]

Out[124]=

-Graphics -

The total population size should be

In[105]:=

6^8

Out[105]=

1679616

which is (just checking) the same as the number of entries in our computer generated population.

In[106]:=

Length[dice]

Out[106]=

1679616

And the population parameters are

In[110]:=

μ8 = Mean[dice] // N

Out[110]=

28.`

In[109]:=

σ8 = StandardDeviationMLE[dice] // N

Out[109]=

4.83045891539648`

In[111]:=

s8 = StandardDeviation[dice] // N

Out[111]=

4.8304603533623816`

Converted by Mathematica  (September 11, 2003)