Due March 7

1) Consider the pdf f(x) = sin(x)/2 for 0 <= x <= PI
                                        0 otherwise

a) Show that the cumulative distribution is given by
F(x) = (1 - cos(x)) / 2 for 0 <= x <= PI, 0 otherwise

b) Using the programming language of your choice, generate 1000 samples of a random variable
that has the pdf specified above. Write them to a file

c) Read that file into excel, and generate a (sorted) histogram of the values.  Experiment with
different bin widths to produce a nice looking histogram

2) Perform the same operations for a random variable given by
pdf  f(x) = (1/1.852)*sin(x)/x for 0 <= x <= PI, 0 otherwise.
Note that there is no closed form anti-derivitive for this function, so it is highly
inconvenient to try to use the inverse of the cdf.