06 04 02 0 0 1 2 3 4 5 crack length mm 6

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Unformatted text preview: the probability density function. b) Graph the cumulative distribution function. ! c) What is the probability that a crack will be smaller than 4 mm? 0.6 0.4 0.2 0 0 1 2 3 4 5 crack length (mm) 6 1/8 CEE 202 – Engineering Risk & Uncertainty Homework 4 Spring 2011 (Bond) Probability Distributions, Expected Values c) We already have an analytic form for Fx(x). P(X<4) = Fx(4) = 4/4 – 0.25 = 0.75 2) An engineer recommends a design snow load of 30 lb/ft2 for a flat ­roofed building in Chicago. (“Design load” means the roof will fail if the load is greater.) The annual maximum snow load X (in lb/ft2) on buildings with flat roofs in Chicago can e modeled by a random variable with the following CDF: F(x) = 0, for x ≤ 10 4 = 1 – (10/x) for x >10 a) Graph the probability density function and the cumulative distribution function. b) What is the probability of roof failure in the first year of operation? c) What is the probability that failure will occur for the first time in the...
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