plugin-HW_05_Solutions

# plugin-HW_05_Solutions - HW #5 Solutions (Fall 2011)...

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HW #5 Solutions (Fall 2011) Assigned problems Ang & Tang: 3.7, 3.14, 3.18, 3.19, 3.26 Not checked 3.7 NOTE: in the problem the range of x is x > 10 not x > 0 (a) The mean and median of X are 13.3 lb/ft 2 and 11.9 lb/ft 2 , respectively (as done in Problem 3-3-3). (b) The event “roof failure in a given year” means that the annual maximum snow load exceeds the design value, i.e. X > 30, whose probability is P(X > 30) = 1 – P(X < 30) = 1 – F X (30) = 1 – [1 – (10/30) 4 ] = (1/3) 4 = 1/81 = 0.0123 Now for the first failure to occur in the 5 th year, there must be four years of non-failure followed by one failure, and the probability of such an event is (1 – p) 4 p = [1 - (3/4) 4 ] 4 (1/3) 4 0.0117 (b) Among the next 10 years, let Y count the number of years in which failure occurs. Y follows a binomial distribution with n = 10 and p = 1/81, hence the desired probability is P(Y < 2) = P(Y = 0) + P(Y = 1) = (1 – p) n + n(1 – p) n – 1 p = (80/81) 10 + 10 (80/81) 9 (1/81) 0.994

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3.14
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## This note was uploaded on 01/02/2012 for the course CIVIL ENG 408 at USC.

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plugin-HW_05_Solutions - HW #5 Solutions (Fall 2011)...

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