304_Exm2_07_forWeb - CEE 304 Uncertainty Analysis in...

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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 landing-weight W times the vertical-landing-speed 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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