P410/P609 Homework Assignment #4
Due Tuesday, November 7, 2006
Problem 1
Complete Problem 4.6 parts a-d on page 93 of CSM.
If you would like to use Mathematica to solve some or all of this problem,
you are welcome to do so. Please note that in part (c) many students in
the past have gotten confused computing the relaxation time. You can only
find the amplitude at the turning points of the motion, i.e., where the
velocity changes time. You can use turning points where the position is
positive or negative. If you make a semilog plot of the absolute value of
these positions vs time, you should find an exponential decay.
Problem 2
Using Mathematica, find the value of the integral of the function sin(x)/x
over the interval [0,5].
Problem 3
The local newspaper carried a story about jury selection for a trial.
The paper stated:
At a hearing Thursday in Owen County, Nardi denied a motion filed by
defense attorneys David Colman and Elizabeth Cure to disqualify the
jury panel. Colman and Cure observed that out of 80 potential jurors,
only one was younger than 30.
"Monroe County has a population of 120,000 people, of which between
30,000 and 40,000 are students at Indiana University," the motion stated.
"A truly random jury-selection process for Monroe County should result
in no fewer than 20 students from Indiana University."
This might be a good time for a lawyer joke, but I will resist that temptation
and ask you to analyze this situtation.
a) Assuming that there are 120,000 people in Monroe county and 30,000 of
those people are students at IU, what is the probability that a group of
80 randomly selected people would include fewer than 20 students?
Note, if you had been among the people called for jury duty, you probably would
have been excused from jury duty if you had pointed out the lawyer how stupid
his statement was. (I got out of jury duty a couple of years ago when I told
the laywer that he had just contradicted himself.)
b) What is the probability if 40,000 of the 120,000 people, that there would be
fewer than 20 students in a randomly selected group of 80 people?
Note: I will be pleased if you can use Mathematica to solve this problem, but
if you prefer another approach, that is also fine. If you have taken a
course in statistical mechanics or a math course that covered combinatorics
you should have the theoretical background for solving this problem. If not,
come see me we can talk about drawers containing red socks and blue socks and
how many ways we can pick socks from the drawer.