CEE 304  Uncertainty Analysis in Engineering
Second Examination
November 9, 2007r
You may use text, your notes and calculators. There are 50 points in total, one per minute. Show work
1. (12 pts) A structural engineer needs to model the cumulated stress on the landing gear of an airplane
design. Aging airplanes pose a risk of failure. The cumulated metal fatigue depends upon F the product of the
landingweight W times the verticallandingspeed S, so that F = W•S. She needs the whole F distribution.
Assume that W and S are independent random variables with lognormal distributions. W has a mean of 120
with a coefficient of variation of 0.20. S has a mean of 35 with a standard deviation of 12.
(a) What is the 95 percentile of the S distribution?
(b) What are the mean and variance of the F distribution?
2. (6 pts) A geotechnical engineer needs to evaluate the properties of soil around a construction site. He
instructs his technician to collect 10 samples. However, the technician is lazy, and also dishonest (and a little
stupid). The technician collects 6 samples, and then adds the four
fixed
values 50, 54, 56, and 60. Suppose
measurements of the soil parameter really have a gamma distribution with a mean μ of 62 and a stand.
deviation of 9. If the engineer computes the sample average A of the ten values [6 measurements, and 4 fixed
values], what is the
mean square error
of his estimator of μ:
A = [ X
1
+ X
2
+ X
3
+ X
4
+ X
5
+ X
6
+ 50 + 54 + 56 + 60]/10
?
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 Fall '08
 Stedinger
 Standard Deviation, Trigraph, Sa mple, distribu tion, mean concentra tion

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