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CEE 304

UNCERTAINTY ANALYSIS
IN
ENGINEERING
FINAL
EXAM
Wednesday, December 8,1993
Exam is open notes and openbook.
The exam lasts 150 minutes and there are 150 poin is.
SHOW WORK!
1.
(10 points) An engineer must use the cumulative distribution function
FX(x)
=
(da
forO~x11
to describe a particular phenomona. Given a random sample of n independent
observations {XI, X2,
...
,
Xn),
what is the maximum likelihood estimator of the
unknown shape parameter a?
2. (10 points)
Please explain in 25 words or less why method of moment
estimators make sense.
3.
(10 points) An engineer is concerned with the loading on a bridge over its
lifetime. Suppose that major dynamic shock loadings can be described by an
exponential distribution with a mean of 4,000. Assume that the bridge would
need to absorb 1000 such shocks over its operational lifetime.
Using the
appropriate asymptotic distribution, what is the mean and variance of the largest
of those 1000 shocks? (Which is the load for which bridge should be designed.)
4.
(5 points)
Of course, large shocks really arrive randomly in time.
If on
average the bridge receives 30 shocks per year, and they occur independently
over time, what is the mean and variance of the time until 1000 shocks occur?
5.
(10 points) Rainfall is often well described by a lognormal distribution.
Assume that the mean and standard deviation of maximum annual 24hour
rainfall depths are 3.1 inches and 1.8 inches. What is the rainfall depth exceeded
with a
1%
probability?
6.
(10 points) Consider 8 individual weights submitted by class members
117
150
162
145
170
125
175
160
Might these be described by a normal distribution? Use the attached probability
paper to construct a visual test of normality.
Indicate the numerical values of
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304

UNCERTAINTY ANALYSlS
IN
ENGINEERING
FINAL
EXAM
Wednesday, December 8,1993
7. (10 points) Twelve women provided their heights; they had a sample mean
of 65.15" and a standard deviation of 2.44".
Let us consider these women to be a
random sample of Cornell women engineering students.
What is a 90%
confidence interval for the true mean height of Cornell women engineering
students? (~ssume
that heights are normally distributed.)
What is the probability that the interval you just constructed actually
contains the mean height of Cornell women engineering students, assuming the
12 who responsed are a representative random sample?
8. (10 points)
Now the big question.
Are men taller than women,
as is often
believed? Look at the data that was turned in on heights:
N

M
MEDIAN
STDEV
Women
12
65.1 46
64.500
2.441
Men
3
1
71.258
71
.OOO
2.889
Use a pooled t test because Nwomen only equals 12.
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 Fall '08
 Stedinger

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