October 9, 2007 --- Class 12 --- Biased Estimators Using Mathematica
Activities:
Biased Esimators Using Mathematica
Dan Beeker was guest lecturer because I was out of town.
We considered the problem posed in section H of the handout.
We started by teaching Mathematica to do multiple integrals
analytically and then having it get a numerical result as described
in the handout.
We trained Mathematica to do multiple integrals analytically
for the problem we are considering. Without
waiting too long, we were able to get up to a sample size of 6;
however, this result still shows significant bias. On the Swain
Apple cluster in October_10_2006.nb you will find a notebook with
the commands I wanted discussed during class.
We found that for small samples sizes, the integrals, which
represent the average value for 1/(mean value) we get numbers
larger than 2, even though for an infinite sample we expect 2.
Some problems with the projector were encountered during class, so
some of the above will be reviewed in the next class.