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homework_10 - MIT OpenCourseWare http/ocw.mit.edu 1.010...

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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 #10 Due December 4, 2008 (in class) 1. Random variables X 1 , …, X 50 are independent with the following distributions: X 1 , …, X 10 U[0, 1] X 11 , …, X 20 N(1, 0.1) X 21 , …, X 30 LN(3, 0.2) X 31 , …, X 40 Ex[0.4] X 41 , …, X 50 Ga(2, 0.2) where U[0, 1] is the uniform distribution in [0,1], N( m , σ 2 ) and LN( m , σ 2 ) are the normal and lognormal distributions with mean value m and variance σ 2 , Ex[ m ] is the exponential distribution with mean value m , and Ga( n , m ) is the gamma distribution that results from adding n iid exponential variables with distribution Ex[ m ]. Find in approximation the 50 probability that Y = " X i exceeds 56. i = 1 2. The daily SO 2 concentration at a given location is normally distributed with mean 0.03 ppm (parts per million) and coefficient of variation 40%. Clean air standards require
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