In a notched tensile fatigue test on a titanium specimen, the expected number of cycles to first acoustic emission (used to indicate crack initiation) is u = 28,000, and the standard deviation of the number of cycles is o = 4000. LetX1, X2, .... X25 be a random sample of size 25, where each X, is the number of cycles on a different randomly selected specimen. Then the expected value of the -Select---number of cycles until first emission isE(X) = µ = 28,000, and the expected total number of cycles for thespecimens is E(T,) = nu = 25(28,000) = 700,000. The standard deviations of X and T, areo, = Vno = V25(4000) = (If the sample size increases to n = 100, E(X) is unchanged but o =

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Answered: In a notched tensile fatigue test on a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a notched tensile fatigue test on a titanium specimen, the expected number of cycles to first acoustic emission (used to indicate crack initiation) isu = the standard deviation of the number of cycles is o 28,000, and 4000. Let X,, X, . . . , X25 be a random sample of size 25, where each X; is the number of cycles on a different Example 5.24 2' randomly selected specimen. Then the expected value of the sample mean number of cycles until first emission is E(X) 28,000, and the expected total = U = number of cycles for the are specimens is E(T,) = nµ = 25(28,000) = 700,000. The standard deviations of X and T, ox = 0/Vn V V 25(4000) = no = If the sample size increases to n = 100, E(X) is unchanged but o , = 800 half of its previous value (the sample size must be quadrupled v to halve the standard deviation of X.)
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