CEE_110_PS4_08_Solutions

CEE_110_PS4_08_Solutions - UNIVERSITY OF CALIFORNIA LOS...

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UNIVERSITY OF CALIFORNIA, LOS ANGELES Civil and Environmental Engineering Department CEE 110 Introduction to Probability and Statistics for Engineers Spring Quarter 2008 M-W 2-4 PM 3400 Boelter Hall Prof. K. D. Stolzenbach 5732J Boelter Hall, 206-7624 [email protected] Problem Set 4 Solutions _____________________________________________________________________________ 1. 22 2 2 200 var(ln x) ln 1 ln 1 0.223 400 0.472 0.223 E(ln x) ln ln(400) 5.88 P(Q 500cfs) 1 P(Q 500cfs) 1 P(lnQ 6.21) lnQ 6.21 5.88 1F 0.472 1 F(0.70) 1 0.7580 0.2420 ⎛⎞ σ = ζ =+=+ = ⎜⎟ μ ⎝⎠ ζ= ζ =λ= μ− = = >= ≤= −λ =− ζ = 2. (a) [] ln(80) P[failure] P R 80kip F − λ =< = ζ 30 cov 0.3 0.30 0.3 100 == = ± σ ζ μ 11 ln ln(100) (0.30) 4.56 λμ = = () ln(80) 4.56 P R 80kip F F 0.59 0.2776 0.3 <= = = (b) [ ] P R 80kip 0.2776 ln(50) 4.56 P R 50kip F F 2.16 0.0154 0.3 = = [ ] P failure 0.3 P[R 50kip] 0.7 P[R 80kip] 0.199 =⋅ < +⋅ < = (c) P[failure | p 50kip] P[p 50kip] P p 50kip | failure P[failure] = ⋅= 0.0154 0.30 P p 50kip |failure 0.023 0.199 =
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3. (a) 1 12 v months = 1 6 12 ( 6 ) 1 0.393 39.3% P T months e −⋅ <= = = (b) (6 | 6 )(6 ) >> = > P T more months T month P T months because the events are independent 1 6 12 ( 6 ) 0.606 60.6% >= = = P T month e (c) 10 10 ( 1) 1 ( 0) 1 ( 6 ) 1 0.606 0.9933 99.3% XX P x P x P T
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This note was uploaded on 05/19/2011 for the course CEE 110 taught by Professor Stolzenbach during the Spring '08 term at UCLA.

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CEE_110_PS4_08_Solutions - UNIVERSITY OF CALIFORNIA LOS...

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