FinalExamSolutions

# FinalExamSolutions - Steven Weber Dept of ECE Drexel...

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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

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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.
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