# CS 147 Homework Assignment 1

This homework assignment is due at 12 AM on Thursday, February 9,
2012 (i.e., the Wednesday/Thursday boundary). Please give your
solutions to me, slide them under my door, or e-mail them.

Most of the problems in this assignment are taken from the textbook. I
expect that it will take you about 2 hours to complete the assignment.

If you use a Microsoft product to do your graphing, be sure to turn
off the stupid gray background, and ensure that color isn't essential
for interpreting the graphs (since I might decide to print things on a
B&W printer).

Problems from the textbook: 12.7 through 12.15.

Additional problems:

- 12.16
- What is the skewness (see box 12.1 on page 197) of the
data from problem 12.15? What is the kurtosis? The
kurtosis is calculated by using an exponent of 4 instead
of 3 in the skewness equation, and then subtracting 3
from the result, as follows:

kurtosis = [ 1/(n*s^4) * sum[(xi-xbar)^4] ] - 3

A skewness significantly far from zero indicates a skewed
distribution. A kurtosis with an absolute value greater
than about 0.5 indicates a distribution narrower
(negative) or wider (positive) than a normal distribution.

**NOTE:** Most authorities suggest dividing
by (n-1) instead of n when calculating both skewness and
kurtosis. For this problem, we'll stick with the biased
estimate (using n) since that's what the book uses.
- 12.17
- Do the skewness and kurtosis you calculated in 12.16
support the conclusions you reached in 12.15?
- 12.18
- (Extra credit.) Plot a kernel density estimate of the
data from problem 12.15, using either a Gaussian or a
triangular kernel. If you used an existing software to
create the plot, identify the package (I'm looking for
good packages).
- 12.19
- (Extra credit.) Derive the formula for the number of
samples needed to demonstrate that one system is better
than another to a given level of confidence.

## Notes:

To save you pointless typing, here are links to the data given in some
of the problems:

12.10
12.11
12.15
For problem 12.7, you may find the tables in Appendix A useful, or you
might choose to use a program with statistical functions (some options
include Excel, Matlab, R, and Minitab). In problem 12.7b, interpret
"less than" as "less than or equal to".

*© 2012, Geoff Kuenning*

This page is maintained by Geoff
Kuenning.