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MIT OpenCourseWare http://ocw.mit.edu 1.010 Uncertainty in Engineering Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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! ! " # & $ $ % ( ) * + , - - 1.010 Fall 2008 Homework Set #7 Due November 6, 2008 (in class) 1. X has uniform distribution between 0 and 1. Let Y = X 2 . a) Find the exact mean value and variance of X b) Find the exact mean value and variance of Y . c) Approximate the mean value and variance of Y using first-order second-moment (FOSM) analysis. Compare with the results in (b). 2. The natural frequency ω at which a one-story building vibrates is given by K ω = M where K is the lateral stiffness of the building and M is its mass. If K is random with mean value m K and standard deviation σ K and M is known, use FOSM analysis to find in approximation the mean value and variance of ω . 3. In planning a building, the number of elevators is chosen on the basis of balancing initial costs versus the expected delay times of the users. These delays are closely related to the number of stops the elevator makes on a trip. If an elevator runs full (n people) and
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