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Assignment 6 solutions

Assignment 6 solutions - CE93-Engineering Data Analysis...

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CE93-Engineering Data Analysis Mark Hansen, Fall 2009 Assignment 6 1. Bay Bridge repairs: Total days (T) days for repair A + days for repair B (T A +T B ) Probabilities g(G) = g(G ± ) ∗ ²(G ³ ) Total probability ∑g(G) 13 6+7 0.06 0.06 14 6+8 7+7 0.08 0.15 0.23 15 6+9 7+8 8+7 0.06 0.2 0.09 0.35 16 7+9 8+8 0.15 0.12 0.27 17 8+9 0.09 0.09 PMF of total duration T to finish both repairs 2. Storm runoff a) Find ´ and draw PDF. Find CDF. Integrate the PDF to find the CDF. If we set the CDF=1 over 0 ≤ µ ≤ 50 , we can find ´ . ¶(µ) = · ¸(µ)¹µ º» » = 1 = · ´ ∗ ¼µ − µ ½ 50 ¾¹µ º» » = ´ ∗ ¼ µ ½ 2 µ ¿ 150 ¾ + ÀÁ » º» = ´ ∗ ¼ 50 ½ 2 50 ¿ 150 ¾ + À 1 = ´ ∗ ¼ 50 ½ 2 50 ¿ 150 ¾ + À But we know À = 0 because ¸(0) must be zero. Therefore, ´ = 0.0024 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 13 14 15 16 17

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CE93-Engineering Data Analysis Mark Hansen, Fall 2009 x pdf cdf 0 0 0 1 0.002352 0.001184 2 0.004608 0.004672 3 0.006768 0.010368 4 0.008832 0.018176 5 0.0108 0.028 6 0.012672 0.039744 7 0.014448 0.053312 b) Find probability that runoff from the storm is less than 40 given that overflow occurs g(G ≤ 40u±²³´µ¶±· ±¸¸¹´º) = g(G ≤ 40uG ≥ 30) =
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