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cee93-spring05-final-Der_Kiureghian-soln

# cee93-spring05-final-Der_Kiureghian-soln - University of...

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University of California at Berkeley Department of Civil & Environmental Engineering Structural Engineering Mechanics & Materials Instructor: Armen Der Kiureghian Student name:__________________________ CE93 -- Engineering Data Analysis Final Examination Tuesday, May 17, 2005 Work on all four problems. Write clearly and state any assumptions you make. The exam is closed books and notes, except for three sheets of paper and the table of Matlabfi dis- tributions. The problems have the following weights: Problem 1 (30 points) ________________________ Problem 2 (20 points) ________________________ Problem 3 (20 points) ________________________ Problem 4 (30 points) ________________________ Exam grade (100 points) ______________________

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Student name:__________________________________ 2 Problem 1. (10+10+10 = 30 points) Timely completion of a construction project depends on the weather and on the working conditions of machinery used on the job. The probabilities of delay for different combina- tions of weather condition (rain or no rain) and machinery breakdown are listed in the fol- lowing table: Weather Machinery Probability of delay in completion of the project No rain No breakdown 0.05 Rain No breakdown 0.20 No rain Breakdown 0.30 Rain Breakdown 0.60 Weather forecast indicates 30% chance of rain. From previous experience, we know that the probability that the machinery will breakdown depends on the weather conditions (due to the added force required to move wet soil). If it rains the probability of breakdown is 0.25, whereas if it does not rain the probability of breakdown is only 0.10. a) Determine the probability that the construction job will be completed on time. b) If the job is known to have been completed on time, what is the probability that it rained? c) If the job is not completed on time, what is the probability that machinery breakdown occurred? Solution Define R = rain, B = Breakdown, D = Delay. a) ) ( ) | ( ) ( ) | ( ) ( ) | ( ) ( ) | ( ) ( B R P B R D P B R P B R D P B R P B R D P RB P RB D P D P + + + = 630 . 0 ) 30 . 0 1 ( ) 10 . 0 1 ( ) ( ) | ( ) ( 225 . 0 30 . 0 75 . 0 ) ( ) | ( ) ( 070 . 0 ) 30 . 0 1 ( 10 . 0 ) ( ) | ( ) ( 075 . 0 30 . 0 25 . 0 ) ( ) | ( ) ( = × = = = × = = = × = = = × = = R P R B P B R P R P R B P B R P R P R B P B R P R P R B P RB P 143 . 0 630 . 0 05 . 0 225 . 0 20 . 0 070 . 0 30 . 0 075 . 0 60 . 0 ) ( = × + × + × + × = D P 857 . 0 143 . 0 1 ) ( 1 = = D P Ans. b) ) ( ) ( ) | ( ) | ( R P D P R D P D R P =