09_Midterm_sol - EECE453 Midterm 2009 Question 1 1. If A...

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Unformatted text preview: EECE453 Midterm 2009 Question 1 1. If A and B are independent events, prove that A and B g are also independent (here B g denote the complement of event B) [sol] G, = G[, ] , where C = whole set = G G, = G [1 G] = GG therefore, A and B g are also independent. 2. A binary source [0,1] transmits with probabilities P(X=0) =3/4 through a channel. Due to noise, the output Y differs from X occasionally. The channel output Y is modeled by conditional probabilities: P(Y=1|X=1) = p 1 and P(Y=0|X=0) = p 1 . where p 1 is the parameter you have computed on page 1. Compute P(Y=1), P(Y=0), and P(X=1|Y=1). [sol] channel matrix = 1 1 = 2/14 12/14 12/14 2/14 = 3/4 1/4 , = = 9/28 19/28 = 1 1 3/4 1/4 G = 1 = ,G = 0 = G = 1| = 1 = , = = 3. A binary source X[K] has transition probability P{(X[K])(X[K-1])} gives by the following matrix 3....
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This note was uploaded on 12/05/2011 for the course EECE 453 taught by Professor Vikram during the Spring '09 term at The University of British Columbia.

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09_Midterm_sol - EECE453 Midterm 2009 Question 1 1. If A...

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