- Helicopter competition. The competition will be hold on 10/20 (Tuesday) in class.
The report is due 10/22 (Wednesday) before 5:00PM:
Read chapter 12 (Helicopter design) and design your helicopter.
You can make two helicopters out of one piece of printer paper.
Print this picture as a guide
to cut paper (I drew this in Powerpoint then printed to pdf. For some reason
some lines didn't extend to the boundry. But I think it should be good
enough for cutting.). Some rules are:
- You are not to modify the "body" in anyway, only adjust "L" and "W" of the wings.
Read this diagram for definitions of "L" and "W".
Note we changed the range of L to be 2~11cm and W to be 1~7cm so
that the optimal values are in the ranges.
- You are allowed NO MORE than 24 helicopters, and no more than 200 flights TOTAL.
For example, you could make 20 helicopters and fly each of them 10 times,
recording their L and W and flight time. Flight times should be
recorded to the nearest hundredth of a second.
- Flights are suppose to be dropped from a height of 9 feet measured from the
ground to the bottom of the copter when being held suspended (preflight).
Form 4 teams with 3 people in each to design your helicopter and compete.
There will be a prize for the winning team.
Each student must write and submit his/her own reports on:
- how you decided on W, L. Hint: consider measurement error, use more than one analysis step to find the max, use Taylor's approximation to approximate the shape of the time of flight curve.
- Draw your estimate of the time of flight surface. But remember your goal is to find the maximum not the entire surface.
- Due 10/8 (Thursday) before 5:00PM:
- Read chapter 11: A Mouse Model for Down Syndrome.
- Do all the excercises and submit anwers for questions:
1, 2, 3, 4, 5 (the way to control multiple test problem in this question
is called "Bonferroni correction") , 6, 8, 10, 17.
- Submit answers to all the questions in "Investigation" section (page 220-221).
The data can be found at
here.
- Due 10/1 (Thursday) before 5:00PM:
- Read chapter 10: Maternal Smoking and Infant Health
(continued).
- Do and submit your answers to all the questions.
Note there's a typo in question 7. The expression in 7.c
should be y - ybar * 1 - b_(yx.1) * (x - xbar * 1).
- Analyze the pollution data
and discuss whether pm10 (pollution measure) is associated
with mortality.
- Due 9/24 (Thursday) before 5:00PM:
- Read chapter 4.
- Do all the excercises and submit your answers for following questions:
1, 2, 4, 5, 6, 7, 8, 10, 16, 17. DNA data for questions 4 and 5 is
here.
- Due 9/17 (Thursday) before 5:00PM:
- Read chapter 5 (the "can she tell the difference?" chapter about testing)
before Contingency Tables section.
- Do all excercise and turn in your answers for following questions:
1, 2, 3, 8, 9, 11.
- What is Poission distribution?
- Using this approximation: lim_n (1- lamba/n)^n -> exp(-lambda) to prove
that if N->inf, p->0, but Np -> lambda then binomial is approximately Poisson.
- Take a random sample of n=25 people from this
medical expenditure data.
Assume the posted data is for the entire population.
- Use the sample to estimate the population average, the standard error of your estimate,
and give a 95% confidence interval. Use the CLT.
- Use the bootstrap to estimate the standard error of your estimate and to
construct a 95% confidence interval. Also use the bootstrap results to assess
the distribution of the sample average.
- Now perform a simulation with the known data to check which
approach provided a better confidence interval.
(Hint: 5.a and b give two ways of computing a 95% CI for the population mean.
Now given the whole population, you can sample 25 people, using two different methods
to compute CIs and check whether they cover the true mean. Repeat the process
for many times and compare the number of times of each CI covering the mean.)
- Due 9/10 (Thursday) before 5:00PM:
- Read Chapter 2 do all problems.
- Turn in your answers for following 10 questions: 1,3,5,7,8,9,12,13,18,23.
Note there seems to be a typo in question 18(c). It should be
x*=x (without 2).
- What is Bernoulli trial?
- What is Stirling's approximation?
- Show that if Sn is the sum of n independent Bernoulli trials with
probabiliy of success 0.5 then
2
√n
(Sn/n-0.5) tends to N(0,1) (the standard normal).
- Due 9/1 (Tuesday)
Read Chapter 1 of Stat Labs and do all the exercises.