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CEE 304  UNCERTAINTY ANALYSIS IN ENGINEERING
2004 Final Examination and Solution
12:00  2:30, Thursday, December 9, 2004r
Exam is open notes and openbook.
It lasts 150 minutes and there are 150 points.
SHOW WORK!
1. (10 pts – 2 pts each.)
Short and trueorfalse answers
a.
The
Student t distribution
was developed by Professors Student & Fisher around 1908 (T/F).
b.The Student t distribution is like the normal distribution, only with a larger variance (T/F).
c.
The Central Limit Theorem
assures us that if one sums up a large number of random variables,
the distribution of the sum will always be normally distributed (T/F).
d. Unfortunately,
nonparametric tests
never have greater power than the corresponding t or z test
(T/F).
e.
An example of a continuous distribution for which the method of moments and maximum
likelihood
estimators
are essentially the same is _____ .
2. (5 pts)
In what fundamental way are probability and statistics different? Recall that they are both about
distributions, frequency, variability, and uncertainty.
3. (10 pts) A structural engineer is modeling the fastest wind gust observed in a year for the purpose of
design of electrical transmission lines. • Assuming that observed annual maxima wind gusts have a
Gumbel distribution with mean 35 mph and standard deviation 12 mph, what wind gust speed has only a
0.1% probability (0.001) of being exceeded in any year? • WHY is a Gumbel distribution a reasonable
model for such phenomena?
4. (10 pts) A company uses an automated sampler with data storage to sample their product during each
of the 6 work days a week (one sample per day). Each week, the sample average of the
6 recorded values is computed. However the student programmer made a mistake causing the first
recorded sample value to always be recorded as 4. (Stupid!) Assume the other five measurements have a
Weibull distribution with population mean equal to the true mean concentration (equal to 11.2), and a
standard deviation equal to 0.34.  Is the average of the six recorded values an unbiased estimator of the
population mean? (explain)  What is the mean square error of the average of the six values when
considered as an estimator of the population mean?
5. (12 pts) A Boy Scout troop is going to bike 220 miles along the the length of the C&O canal.
Because of the crushed rock surface of the bike path, the trip is hard on bicycle tires and the group is
likely to experience one flat tire on average every 90 miles.
(a) Why might a Poisson process be a reasonable model for the arrival of flat tires?
Why might such a model not be appropriate?
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View Full Document CEE 304  UNCERTAINTY ANALYSIS IN ENGINEERING
2004 Final Examination and Solution
12:00  2:30, Thursday, December 9, 2004r
Assuming a Poisson process
(b) What is the mean and variance of the number of flat tires they will experience over the course
of the 220 mile trip?
(c) The scoutmaster hates patching bike tire tubes on the road, so that he carries with him 3 extra
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This note was uploaded on 02/02/2008 for the course CEE 3040 taught by Professor Stedinger during the Fall '08 term at Cornell University (Engineering School).
 Fall '08
 Stedinger

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