•Estimation of Population Parameters (μ,σ) from Sample Statistics (m,s)

For example, suppose we didn't know the result for 8 dice, and wanted to find out what it was.  Well then, roll eight dice a few times, call that your sample, and then use those numbers to estimate (i.e. guess) what the real results are.

In[127]:=

rollDice[n_] := Sum[Random[Integer, {1, 6}], {n}] ; diceSample = Table[rollDice[8], {10}]

Out[128]=

{27, 23, 28, 34, 23, 36, 23, 35, 35, 30}

What that just did was find the sum of 6 dice (random integers from 1 to 6) ten times.

In[130]:=

Mean[diceSample] // N

Out[130]=

29.4`

In[131]:=

StandardDeviation[diceSample] // N

Out[131]=

5.3582750126426975`

The true values which we found before are 28.0 and 4.83, so you see that we came pretty close even with only 10 randomly chosen members of the entire population of 1.7 million .  


Converted by Mathematica  (September 11, 2003)