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CEE 202 HW 4 Solutions

# Px 30 1 px 30 1 fx30 1 110304

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Unformatted text preview: fifth year of the building’s operation? 2.a) dF ( x) f ( x) = dx Ⱥ f ( x) = 0 Ⱥ Ⱥ 4 ⋅10 4 f ( x) = Ⱥ x5 Ⱥ for for x ≤ 10 x > 10 2/8 CEE 202 – Engineering Risk & Uncertainty Homework 4 Spring 2011 (Bond) Probability Distributions, Expected Values b) Roof fails if the load is greater than 30 lb/ft2. p(X > 30) = 1  ­ p(X ≤ 30) = 1 – Fx(30) = 1 – (1 ­(10/30)4) = 1 ­0.988 = 0.012 c) Assume that the probability of the roof failing in any given year is the same, and that the probabilities between years are independent P(fail5th for the first time) = P(nofail1th) P(nofail2nd) P(nofail3rd) P(nofail4th) P(fail5th) = (1 – P(Fail))4 P(Fail)= 0.9984 * 0.012 = 0.0117 3) The proportion of budget (Y) for solvent manufacturers that is allotted to pollution control is of concern. A data collection project determines that the probability distribution of Y is given by f(y) = 6 (1 ­y)5, 0 ≤ y ≤ 1...
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