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Unformatted text preview: EE 278 October 28, 2009 Statistical Signal Processing Handout #11 Sample Midterm Examination Problems The following are old midterm problems. The midterm will cover lecture notes 15, pages 16 of lecture notes 6, and homeworks 15, including the Schwarz and Jensen inequalities and the extra problems. These problems are meant for practice. The actual midterm will have fewer problems. 1. Inequalities. Label each of the following statements with =, , , or None . Label a statement with = if equality always holds. Label a statement with or if the corresponding inequality holds in general and strict inequality holds sometimes. If no such equality or inequality holds in general, label the statement as None . Justify your answers. a. P( A ) vs. 1 (P( A c ,B ) + P( A c ,B c )). b. E( X 1 X 2  X 3 ) vs. E( X 1  X 3 ) E( X 2  X 3 ) if X 1 and X 2 are independent. c. E[Var( X  Y,Z )] vs. E[Var( X  Y )]. d. E[Var( X  Y )] vs. E[Var( X  g ( Y ))]. (Hint: use the result of part (c).) e. E Z [E( X 2  Z ) E( Y 2  Z )] vs. [E Z (Cov( X,Y  Z ))] 2 ....
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This note was uploaded on 11/28/2009 for the course EE 278 taught by Professor Balajiprabhakar during the Fall '09 term at Stanford.
 Fall '09
 BalajiPrabhakar
 Signal Processing

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