Exam1_07

# Exam1_07 - CEE 304 Uncertainty Analysis in Engineering...

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CEE 304 – Uncertainty Analysis in Engineering Prelim 1 October 3, 2007 SHOW WORK. You may use the text, your notes, and calculators. No laptops or cell phones. There are 50 points in total. You have 50 minutes. 1. (8 pts) There are three events of interest, A, E, and H. You know that P(A) = 0.3, P(E) = 0.6, P(H) = 0.8, as well as P(H|E) = 0.667, and P(A E) = 0.15. (a) In the long run, what is the probability that either event A or E or both occur? (b) What is the probability that both H and E occur? (c) If E is known to have occurred, what is the probability that A occurs? (d) What is the probability that neither H or E occur. (No point in H and no point in E.) 2. (8 pts) Scoutmaster Stedinger’s Boy Scouts are selling popcorn. The Trojan and Spartan patrols are expected to sell 100 and 150 boxes of popcorn each with standard deviations of 20 and 25 boxes, respectively, and a correlation of 0.70 between their sales numbers. (a) If sales are normally distributed, what is the probability the Trojans sell more than 135 boxes? (b) If a box of popcorn costs \$10, what are the mean and variance of total sales by the two patrols? 3. (17 pts) A new Tsunami alert system is being developed. The monitoring network is very sensitive and can detect the passage of minor tsunami waves. Still it is thought that only 6 detectable waves will occur every decade. (a) If the network is started tomorrow, what is the pdf for the time that will pass before the 8 th wave is detected? What are the mean and variance of that distribution? (b) What are the mean and variance of the number of waves that will be detected in the next 3 years?

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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.

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Exam1_07 - CEE 304 Uncertainty Analysis in Engineering...

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