CEE_110_PS4_08_Solutions

CEE_110_PS4_08_Solutions - UNIVERSITY OF CALIFORNIA, LOS...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 stolzenb@ucla.edu 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 =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

CEE_110_PS4_08_Solutions - UNIVERSITY OF CALIFORNIA, LOS...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online