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# mtsamp - EE 278 Statistical Signal Processing Sample...

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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 1–5, pages 1–6 of lecture notes 6, and homeworks 1–5, 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 . f. E parenleftBig log 2 parenleftBig 1 + X parenrightBigparenrightBig vs. 1 if X 0 and E( X ) 1.

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mtsamp - EE 278 Statistical Signal Processing Sample...

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