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Unformatted text preview: CEE 304 - UNCERTAINTY ANALYSIS IN ENGINEERING 2006 Final Examination 2:00 - 4:30 pm, Thursday, December 7, 2006 Exam is open notes and open-book. Exam lasts 150 minutes and there are 150 points. SHOW WORK! 1. (20 pts) A hydrologic engineer is concerned with the maximum flood flow in a year and the effect it might have on several riverine structures. An analysis of flood records for the basin indicates that the maximum annual flood Q has a mean of 140 cms and a standard deviation of 35 cms. (a) Using a Gumbel distribution for the annual maximums, what threshold has a 2% probability of being exceeded in any year? (b) WHY is a Gumbel distribution a reasonable model for such phenomena? (c) What value would you get for the flow threshold exceeded with a 2% probability if instead of a Gumbel distribution, one used a lognormal distribution to estimate flood risk? (d) If the annual maximum stage S (a measure of depth) of the water equals 54 Q 0.60 for annual maximum flood Q , and if the maximum flows Q have the lognormal distribution as in (c), what is the mean and standard deviation of the annual maximum stage S ? (f) If a facility is located where it has a probability of 4% of being flooded each year, and floods are independent year-to-year, what is the probability the facility is flooded exactly once in 20 years? 2. (15 pts) For a project, students need to demonstrate that they can evaluate the statistical properties of estimators. Suppose that the goal is to develop a statistically efficient estimator of the average weight of a student at Engineering State College using stratified sampling. In particular the proposed estimator M is the average of the weight of three randomly selected men and two randomly selected women, so that: M = [X 1 + X 2 + X 3 + Y 1 + Y 2 ] / 5 Please use the data below in your computation, along with the observation that at Engineering State College 70% of the engineering students are men and 30% women. Men Women All Students Mean 175 120 158.5 SD 28 21 36.3 (a) What is the mean and variance of the estimator M? (b) What is the bias and mean square error of M as an estimator of the average weight of students? (c) What is stratified sampling? What does it accomplish? How does it do that? 3. (5 pts) Six civil engineers (Kara, Virginia, Mary, Jeremy, Laura and Jery) formed a volleyball team that participated in Cornells intramural league. A coach used a radar speed sensor to measure the velocity of the ball when our civil engineers spiked the other team. Based on a sample of 11 CEE 304 - UNCERTAINTY ANALYSIS IN ENGINEERING 2006 Final Examination Page 2 of 4 spikes, with an observed sample average of 32.4 ft/sec, and a sample standard deviation of 7.6 ft/sec. What is a 98% confidence interval for the true mean velocity of spikes by our civil team?...
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