CSI 779, Spring 1995, J. E. Gentle

Assignment due Feb 13

The integral of x*exp(-x)/(1 + exp(-x))^2 over the real line that was in
last week's assignment can be evaluated very easily in Maple.

Unfortunately, I have not been able to locate Maple on any GMU computer
except osf1.  (It was on the NeXT machines of the science network last
summer, but it's not there now, and I have been unable to find the
system engineers.) I think it might be somewhere else here, so I'll keep
looking.  I have my own copy on my PC.  If you have an account on osf1,
and want to use it, just type maple.  If you have access to Maple
somewhere else, try it there.

After Maple fires up, type

  int(x*exp(-x)/(1 + exp(-x))^2, x=-infinity..infinity);

Maple will print out the answer: 0  (On my Pentium this happens so fast
the "hourglass" is barely seen -- on osf1, it will take a little
longer.)

Then type 

  int(exp(-x)/(1 + exp(-x))^2, x=-infinity..infinity);

(You should know what this answer is!)

Then type 

  int(exp(-x)/(1 + exp(-x))^2, x=-infinity..t);

What is this???? (hint, Maple prints out -arctan(exp(-t)) + Pi/2, in a
graphics mode, so "Pi" is printed as a "pi".  Again, this happens
immediately on my PC, but takes a little longer on osf1.)

Here are a couple of things to do just to practice finding information
on the net.

For this assignment, you are to produce two small items and put
them in a single file that you will email to me.  Each item should be
preceeded by a line that consists of three asterisks and the problem
number, e.g., for the first problem:
*** 1

1.  Use anonymous ftp to get the file using-emacs.txt from 
    pilot.njin.net in the directory /pub/Internet-course.
    List the last 10 lines of this file.

2.  Use anonymous ftp to get the abstracts for the articles published in
    Volume 2, Number 2 of the Journal for Computational and Graphical 
    Statistics.  Extract the abstract for the article on computing an
    Edgeworth expansion, by Kabaila.
    (The abstracts for JCSG are in a directory, with an obvious name,
    that you can get at from the anonymous ftp site for all kinds of
    good statistics stuff:  lib.stat.cmu.edu.)