cee93-Spring_2005-mt2-Armen_Der_Kiureghian-soln

# cee93-Spring_2005-mt2-Armen_Der_Kiureghian-soln - Student...

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Problem 1. (20+10 = 30 points1 The radioactivity of a material at time t is given by the formula R, = Ro exp(-At) where Ro is the radioactivity at time t = 0 and A is the rate of percent decay per unit time. Suppose Ro and A are random variables with the second moments listed below: a) For t = 10, using first-order approximations, determine the mean and standard devia- tion of R, and the correlation coefficient between R, and A. b) Determine the relative importance of the random variables Ro and A in contributing to the variability of R, . Variable R o A a) pR, E 100 x exp(-0.05 x 10) = 60.653 Ans. Standard deviation 3 0 0.02 Mean 100 0.05 o; E (0.607)'(30)' + (-606.530)'(0.02)' + 2(0.607)(-606.530)(0.3)(30)(0.02) = 331.091 +147.152-132.437 = 345.806 oRl =18.6 Ans. - 0.133 PRfA (18.6)(0.02) =-0.358 Ans. Correlation coefficients b) Imp(R,) = 10.6071 x 30 = 18.196, Imp(A) = 1- 606.5301 x 0.02 = 12.131 Imp(R, ) > Imp(A) Ans. R

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cee93-Spring_2005-mt2-Armen_Der_Kiureghian-soln - Student...

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