hw6.pdf - UNIVERSITY OF CALIFORNIA SAN DIEGO Department of Structural Engineering SE125 Fall Quarter 2018 Instructor Joel P Conte SE 125 Statistics

# hw6.pdf - UNIVERSITY OF CALIFORNIA SAN DIEGO Department of...

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UNIVERSITY OF CALIFORNIA, SAN DIEGO SE125 - Fall Quarter 2018 Department of Structural Engineering Instructor: Joel P. Conte SE 125: Statistics, Probability and Reliability Homework Set # 6, due on Monday December 3 Problem 1 The random variable X is Gaussian with a mean X 30 P and a standard deviation X 6 V . Derive the CDF and PDF of X, in this order, conditional on the event ^ ` E 28 X 38 ± d . Plot ² ³ X|E f x | E and ² ³ X|E F x | E using Matlab. Problem 2 The kinetic energy of a particle with mass m and velocity V is given by 2 mV X 2 Suppose that m is deterministic (constant) and V is random with PDF given by ² ³ 2 2 bv V for v 0 a v e f v elsewhere 0 , , ´ ­ ! ° ® ° ¯ Determine the PDF of X, ² ³ X f x . Problem 3 The random variable X is normally distributed with mean X 1 P and standard deviation X 1 V . Let Y 2X Derive the CDF of Y, ² ³ Y F y , and the PDF of Y, ² ³ Y f y , in that order. Plot ² ³ Y F y and ² ³ Y f y using Matlab.

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• Fall '08
• Conte,J

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