HW #1 Due Wed 1/21/04 4 p.m. Stat 310 D.Scott
Note: This homework is shortened due to the holiday next Monday. Expect more problems
in the future. Each problem counts equally (10 points). This homework may also be turned
in during class 1/20 or to my office before 4:00 p.m. on Wednesday 1/21.
1. Conduct a simulation (physical, not computer) of the stick-dropping experiment de-
scribed in class. Repeat 25 times. Report the fraction of times the stick crossed a
line, and provide an estimate of π.
2. Conduct a second simulation: on a flat, smooth table surface, spin a nickel on its side
twenty-five (25) times and record the number of “heads.” (n.b. do not flip the coin
in the air)
3. An ambulance is located at the origin (0,0) and responds to emergencies in the square
[−1,1] ×[−1,1]. The ambulance can only travel east-west and north-south (making
sharp right angle turns). Thus the ambulance must travel a distance of 2 to reach
any of the four corners. Suppose a new emergency occurs “at random” in the interior
of the square. Compute the probability, p(d), that the ambulance will have to travel
less than the distance “d” to reach the location of the emergency. Sketch the function
p(d) for 0 ≤d≤2. Show your derivation.
Bonus Extra-Credit Problems (if you have a clear crystal ball):
4. Predict the closing DJI average for Fridays 1/23 and 4/16 Briefly indicate the (intu-
itive) basis of your predictions. (25 HW bonus points awarded if within 20 and 100
points, respectively, or closest 5 predictions.)
5. Predict the date when the New York Times first states that so-and-so has wrapped
up the Democratic primary race. If you think the date will be later than April 16,
give 4/16. (25 HW bonus points awarded if within 2 days, or closest 5 predictions.)
6. Who do you believe the Democratic candidate will be?