mini_quiz_5

mini_quiz_5 - found to be acceptable? Hint: First find such...

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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 – Mini-Quiz #5 (45 min – open books and notes) Problem 1 (60 Points) Two concrete beams have strengths a n d with joint normal distribution: 1 X 2 X 1 0.75 0.75 1 , 3 3 N ~ 2 X 1 X (in some appropriate units) You intend to use beam 1 for construction. For structural competency, its strength must exceed 2 with probability at least 0.99, i.e. . 99 . 0 ] 2 1 X [ P > a. Find . If this value is less than 0.99, beam 1 cannot be used, unless more information is obtained on its strength. ] 2 1 X [ P > b. To get more information on , you test the second beam. 1
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Unformatted text preview: found to be acceptable? Hint: First find such that . Then calculate . * 2 x 99 . ] * 2 x 2 X | 2 1 X [ P = = > ] * 2 x 2 X [ P = Problem 2 (40 Points) The strength X of a concrete batch has normal distribution where is known ( =1000 psi (pounds per square inch)) but m is uncertain with normal distribution . To better constrain m, you test 4 concrete cylinders in the lab from which you obtain the sample average ) 2 , m ( N ~ X ) 2 ) psi 800 ( , psi 5000 ( N ~ m = 4 i i X 4 1 X . Notice that X has distribution ) 2 4 , m ( N ~ X and that it can be thought of as a noisy measurement of m, + = m X , where ) 2 4 , ( N ~ . Suppose that you measure psi 6000 X = . Find the mean value and variance of ) psi 6000 X | m ( = ....
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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mini_quiz_5 - found to be acceptable? Hint: First find such...

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