Mid Term Solutions

Mid Term Solutions - 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, 2010) Midterm Exam Solutions Instructions: There are five problems. You must answer three of them. Place a LARGE “X” through the two problems you do not wish to be graded. 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 April 23, 2010
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Dept. of ECE Drexel University Name: Student ID #: Score: Problem 1 (4 points) Consider two dependent events A,B . Suppose P ( A ) = p and P ( B | A ) = q and P ( B | ¯ A ) = r (here ¯ A is the complement of A ). Find an expression in terms of p,q,r for P ( A B | A B ) . (1) Give a clear derivation of the expression with each step labeled (e.g., definition of conditional expectation, law of total probability, etc.). P ( A B | A B ) = P (( A B ) ( A B )) P ( A B ) (definition of conditional probability) = P ( A B ) P ( A B ) ( C D C D = C ) = P ( B | A ) P ( A ) P ( A B ) (definition of conditional probability) = P ( B | A ) P ( A ) P ( A B | A ) P ( A ) + P ( A B | ¯ A ) P ( ¯ A ) (law of total probability) = P ( B | A ) P ( A ) P ( A ) + P ( B | ¯ A ) P ( ¯ A ) = qp p + r (1 - p ) (2)
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Mid Term Solutions - Steven Weber Dept of ECE Drexel...

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