Mid Term Solutions

Mid Term Solutions - Steven Weber Dept of ECE Drexel...

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

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

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

View Full Document
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)
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

Mid Term Solutions - Steven Weber Dept of ECE Drexel...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online