FinalExamSolutions

FinalExamSolutions - Steven Weber Dept of ECE Drexel...

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

View Full Document Right Arrow Icon
Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008) Final Exam Solutions (Monday, June 9) Instructions: There are four problems. You have 120 minutes to complete the exam. You are not to use any notes, books, or calculators. Partial credit is given for answers that are partially correct. No credit is given for answers that are wrong or illegible. Write neatly. Name: Student ID #: Signature: Problem 1: Problem 2: Problem 3: Problem 4: Total: www.ece.drexel.edu/faculty/sweber 1 June 9, 2008
Image of page 1

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

View Full Document Right Arrow Icon
Steven Weber Dept. of ECE Drexel University Name: Student ID #: Score: Problem 1 (10 points) Consider the following CDF: F ( x ) = 0 , x < 0 1 2 x 2 , 0 x 1 - 1 2 x 2 + 2 x - 1 , 1 x 2 1 , x > 2 (1) 1. (2 points) Compute the PDF. Make sure to specify the support of any function you write down. Note: full credit for the remaining parts of this question requires a correct PDF, so please make sure your PDF given above is correct. It may help to sketch the PDF. f ( x ) = x, 0 x 1 2 - x, 1 x 2 0 , else (2) 2. (2 points) Verify that the PDF integrates to one. 2 0 f ( x )d x = 1 0 x d x + 2 1 (2 - x )d x = 1 2 x 2 1 0 + 2 x - x 2 2 2 1 = 1 . (3) 3. (2 points) Compute the mean, E [ X ] . Hint: split the integral over [0 , 2] into two integrals, one over [0 , 1] , and the other over [1 , 2] . E [ X ] = 2 0 xf ( x )d x = 1 0 x 2 d x + 2 1 x (2 - x )d x = 1 3 x 3 1 0 + x 2 - 1 3 x 3 2 1 = 1 (4) 4. (2 points) Compute the variance, Var( X ) . Hint: again, split the integral into two parts.
Image of page 2
Image of page 3
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