Data Analysis Homework

Spring 2003

Assignment

• Take the data set (about 10,000 points) and plot a histogram of the sample distribution using at least 50 bins.

• Fit the sample distribution using $f(E)\; =\; f$₀ + f₁*exp(-(E-E₀)²/(2σ²)) and determine the best fit value and estimated error for $f$₀ , $f$₁ , $E$₀ , and $\sigma$.

• Prepare your report on a computer. Graduate students should use latex.

• Graduate students should email the results to me as a pdf or postscript file. Undergraduate Students may give me a hardcopy, however an pdf or postscript is better.

The purpose of this assignment is to understand how to fit a non-linear curve to data. You will need to find an analysis package, or write a program to perform the fit.

I have done example solutions for a different data set generated using a different random distribution.

• PAW:

  The solution in a pdf file or a postscript file for the example problem generated using PAW. The latex source and to PAW kumac file are pretty well documented. I generated the solution using the commands:

  latex solution_paw.tex && latex solution_paw.tex && dvips solution_paw.dvi && ps2pdf solution_paw.ps

  These commands worked on Debian/GNU, but should also work on Redhat.

• MAPLE:

  A worksheet with the solution using Maple 8 is available. This doesn't include the full discussion that I wrote for paw. You'll notice how much more clumsy the solution is in maple, but it is still relatively simple to work with. It runs a little slowly, so be patient.