Exam1_05 - CEE 304 Uncertainty Analysis in Engineering...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CEE 304 – Uncertainty Analysis in Engineering Prelim #1 October 5, 2005 You may use the text, your notes, and calculators. There are 50 points in total. You have 50 minutes. 1. (6 pts) Consider three events denoted ε , η , and τ , where ε and τ are independent, and you know P[ ε ] = 0.5, P[ η ] = 0.7, P[ τ ] = 0.4, P[ ε η ] = 0.3 (a) If ε occurs, what is the probability that τ also occurs? (b) If ε didn’t occur, what is the probability of η ? (c) What is the probability that either ε occurs or η occurs, but not both? 2. (8 pts) A simple model of annual maximum flood events is F = 1.3 A – 0.7 R, wherein A is the area of the watershed and R is a measure of the runoff. The random variables A and R are both normal, such that A ~ N[ 1730, (12) 2 ] and R ~ N[ 2.7, (1.1) 2 ]. Also, Correlation[A, R] = 0.60. What size flood should an engineer design for such that it will be exceeded with a probability of 1% (P[ F f ] = 0.01)? 3. (10 pts) Leak detection is a major problem for older sewer systems. In one city, crews discover leaks at an average rate of 2 leaks per 5-day work week.
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern