PROJECTS
Please note: The projects for 437 and 537 are different. Know the course number for which you have registered.
MATH 437:
In many applications, scientists try to understand ``what's normal' and
what is ``outside the usual profile''. This applies to human lifespan,
quality of silicon chip production, or economic forecasting. When
all is said and done, one essential problem the scientists face is
measuring a sample. If we (i) assume a Gaussian distribution (i.e., a
bell-shape) and (ii) normalize everything in sight, we wind up
looking at integrals like 
. In particular, they
would like to evaluate this integral for various limits of integration.
Obviously this integral is symmetric about the origin.
Normalizing again, the essential problem comes down to finding what limits of integration are necessary for the integral to be, say, 1. To solve this problem, define
Your assignment, then, is to find for what x is F(x)=1?
MATH 537
Read the article by Groetsch. Look at the data sets available on the next webpage, and find the density w(s).
NOTE: Although the matrix A is positive definite, the algebraic problem is ill-conditioned. You should think hard about how you can make the problem less badly conditioned.