lab #9 worksheet
----------------

- make a new folder for week 9

- files for this week:

  w9edf1.m  w9edf2.m  w9edf3.m

- start matlab & change to the
  week 9 folder

KEY QUESTION:  what is the meaning of
those goodness-of-fit quantities, W^2 
and r^2?


warm-up
-------

run each of the w9edf#.m scripts
in order.  they should reproduce
professor stephens' good example
from yesterday.  (with the exception
of a now corrected r^2 value.)

be sure you understand the meaning of
each of the plots.

calculate the W^2 for the data of 
w9edf2.m (it should be 0.0553).

calculate the r^2 for the data of
w9edf3.m (it should be 0.9064).


STUDY #1
--------

w9edf1.m draws a random sample of
25 exponentially distributed (mu=1)
values.  when you calculate the EDF,
it should approximately look like
the theoretical CDF F(x)=1-exp(-mu*x).

but it will not be exactly the same,
and the W^2 will be small (hopefully)
but not zero.  in fact, the values of
W^2 themselves have some CDF!  your 
task will be to compute many different
(don't reset the random seed!) samples,
and build an EDF of W^2 values, until
it looks reasonably smooth and you can
give:

the "quartile" values of W^2 below which
you will find 25%, 50% and 75% of random
samples of 25 exp. dist. values.  

also, what happens to the W^2 EDF as you 
increase the number of random #s in your 
sample (Nrand)?


STUDY #2
--------

repeat the exercise of #1 to construct the 
EDF of n(1-r^2) values.  give the quartile 
values.


SUMMARY
-------

we are currently preparing a group of 12 
data sets of 25 random numbers.  you will be 
asked to determine which of the 12 data
sets are least likely to have come from an 
exponential distribution (mu=1).