A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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3.14 A structure with a design life of 50 yr is planned for a site where high-intensity earthquakes may occur with a return period of 100 yr. The strueture is designed to have a 0.99 probability of not suffering damage within its design life. Damage effects between earthquakes are statistically independent. (a) If the occurrence of high-intensity earthquakes at the site is modeled by a Bernoulli sequence, what is the probability of damage to the structure under a single earthquake? (b) Using the damage probability to a single earthquake from Part (a), what would be the probability of damage to the structure in the next 20 yr, assuming that the occurrences of earthquakes constitute a Poisson process?
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Transcribed Image Text:3.14 A structure with a design life of 50 yr is planned for a site where high-intensity earthquakes may occur with a return period of 100 yr. The strueture is designed to have a 0.99 probability of not suffering damage within its design life. Damage effects between earthquakes are statistically independent. (a) If the occurrence of high-intensity earthquakes at the site is modeled by a Bernoulli sequence, what is the probability of damage to the structure under a single earthquake? (b) Using the damage probability to a single earthquake from Part (a), what would be the probability of damage to the structure in the next 20 yr, assuming that the occurrences of earthquakes constitute a Poisson process?
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