{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CEE_110_PS4_08_Solutions

# CEE_110_PS4_08_Solutions - UNIVERSITY OF CALIFORNIA LOS...

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

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. 2 2 2 2 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 2 2 P(Q 500cfs) 1 P(Q 500cfs) 1 P(lnQ 6.21) lnQ 6.21 5.88 1 F 1 F 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 2 2 1 1 ln ln(100) (0.30) 4.56 2 2 λ μ ζ = = = [ ] ( ) 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 = = =

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

View Full Document
3. (a) 1 12 v months = 1 6 12 ( 6 ) 1 0.393 39.3%
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern