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Unformatted text preview: Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Midterm Exam #2 Solutions Instructions: There are three problems. You must answer all of them. You have 50 minutes to complete the exam. You are not allowed to use any books, notes, or calculators other than your 3 5 note card. 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: Problem 5: Total: www.ece.drexel.edu/weber 1 May 21, 2010 Steven Weber Dept. of ECE Drexel University Name: Student ID #: Score: Problem 1 (4 points) The entropy of a discrete random variable X with pmf p = ( p ( x ) ,x X ) is defined as: H ( X ) = E [- log 2 p ( X )] =- X x X p ( x )log 2 p ( x ) . (1) For example, for a Bernoulli rv X Ber( p ) , i.e., X = 1 , w.p. p , w.p. 1- p (2) we have H ( X ) = H b ( p ) - p log...
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