Exam1_05

# Exam1_05 - CEE 304 Uncertainty Analysis in Engineering...

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CEE 304 – Uncertainty Analysis in Engineering Prelim #1 October 5, 2005 You may use the text, your notes, and calculators. There are 50 points in total. You have 50 minutes. 1. (6 pts) Consider three events denoted ε , η , and τ , where ε and τ are independent, and you know P[ ε ] = 0.5, P[ η ] = 0.7, P[ τ ] = 0.4, P[ ε η ] = 0.3 (a) If ε occurs, what is the probability that τ also occurs? (b) If ε didn’t occur, what is the probability of η ? (c) What is the probability that either ε occurs or η occurs, but not both? 2. (8 pts) A simple model of annual maximum flood events is F = 1.3 A – 0.7 R, wherein A is the area of the watershed and R is a measure of the runoff. The random variables A and R are both normal, such that A ~ N[ 1730, (12) 2 ] and R ~ N[ 2.7, (1.1) 2 ]. Also, Correlation[A, R] = 0.60. What size flood should an engineer design for such that it will be exceeded with a probability of 1% (P[ F f ] = 0.01)? 3. (10 pts) Leak detection is a major problem for older sewer systems. In one city, crews discover leaks at an average rate of 2 leaks per 5-day work week.

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• Fall '08
• Stedinger
• Probability theory, pts, probability density function, Cortland, Jeff ∩ Cort

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