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.