Question: Problem 2. Consider the site located at 50 km distance from one end of a 200 km long fault. An earthquake on the fault

Problem 2. Consider the site located at 50 km distance from one

Problem 2. Consider the site located at 50 km distance from one end of a 200 km long fault. An earthquake on the fault may occur as a rupture of length S, where S is a random variable with PDF fs (s) = 10 kms 100 km $2 The rupture may occur anywhere within the fault with equal likelihood. 50 km site R 200 km rupture. www fault S (a) Determine the parameter k. (b) Derive the conditional CDF and PDF of the shortest distance from the structure to the rupture, denoted R, given that S = s. Sketch the conditional PDF of R for s = 50 km. (c) Derive the joint PDF of R and S. Make a qualitative 3D sketch of this PDF. (d) Determine the numerical values of the following probabilities: 1 Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign CEE 491 Decision and Risk Analysis Instructor Paolo Gardoni P (R75 km S = 50 km) P (R75 km) + In (a+bu). You may use the relation (a+b) du au

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