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Unformatted text preview: EE 178 Tuesday, February 5, 2007 Probabilistic Systems Analysis Handout #8 Sample Midterm Problems The following are old midterm problems. The midterm is on material covered in Lecture Notes 1, 2, and 3 up to page 11, and Homeworks 1-4. 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 strict inequality is possible. If no such equality or inequality holds in general, label the statement as NONE. Justify your answers. a. P( A B ) vs. P( A ) + P( B )P( A c ) if A and B are independent. b. P (( A B ) c ) vs. P( A c ) + P( B c ). c. p X ( x ) vs. p X,Y ( x, y ), for X , Y discrete random variables. d. p Y ( y ) vs. p Z ( g ( y )) if Z = g ( Y ). e. E( X 2 ) vs. Var( X ). 2. Channel with dependent errors. A 3-bit sequence is received over a binary channel with dependent bit errors. The probability that bit 1 is in error is 0 . 2. If bit i , i = 1 , 2, is in error, the conditional probability that bit i + 1 is in error is 0 . 4, and if bit i , i = 1 , 2, is correctly received, the conditional probability that bit i + 1 is also correctly received is 0 . 9. Denote by E i , i = 1 , 2 , 3, the event that bit...
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This note was uploaded on 09/29/2008 for the course EE 178 taught by Professor Hewlett during the Spring '08 term at Stanford.
- Spring '08