Assume that in earthquake-resistant design, the following relations take place: Y=ce, where Y is the ground motion intensity at the building site, X is the magnitude of an earthquake, and the constant c is related to the distance between the site and center of the earthquake. Assuming that X is exponentially distributed, fx (x)=ex with x 20 and >2, (a) Derive the PDF and CDF of Y, including the bounds, and sketch them. (b) Determine the median (i.e., 50%-fractile) and 90%-fractile (value of Y that has a probability of not being exceeded of 90%) of Y. (c) Determine the mean and variance of Y by using the PDF of Y derived under (a). (d) Determine the mean and variance of Y directly from the PDF of X.
Assume that in earthquake-resistant design, the following relations take place: Y=ce, where Y is the ground motion intensity at the building site, X is the magnitude of an earthquake, and the constant c is related to the distance between the site and center of the earthquake. Assuming that X is exponentially distributed, fx (x)=ex with x 20 and >2, (a) Derive the PDF and CDF of Y, including the bounds, and sketch them. (b) Determine the median (i.e., 50%-fractile) and 90%-fractile (value of Y that has a probability of not being exceeded of 90%) of Y. (c) Determine the mean and variance of Y by using the PDF of Y derived under (a). (d) Determine the mean and variance of Y directly from the PDF of X.
Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN:9781305635180
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Braja M. Das, Nagaratnam Sivakugan
Chapter10: Shear Strength Of Soil
Section: Chapter Questions
Problem 10.24CTP
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Transcribed Image Text:Assume that in earthquake-resistant design, the following relations take place: Y=ce, where Y is the
ground motion intensity at the building site, X is the magnitude of an earthquake, and the constant c is
related to the distance between the site and center of the earthquake. Assuming that X is exponentially
distributed, fx (x)=ex with x 20 and >2,
(a) Derive the PDF and CDF of Y, including the bounds, and sketch them.
(b) Determine the median (i.e., 50%-fractile) and 90%-fractile (value of Y that has a probability of not
being exceeded of 90%) of Y.
(c) Determine the mean and variance of Y by using the PDF of Y derived under (a).
(d) Determine the mean and variance of Y directly from the PDF of X.
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