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HW2_Spring11_sol

# HW2_Spring11_sol - ELEC210 Spring 2011 Homework 2 Solution...

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1. A te and (a) (b) ernary comm 2 occur wit Find the pr Suppose th 1? 2? (12) Solution: Let X deno (a) [ p Y p Y = ( 1 1 2 = Similar [ p Y p Y = 1 2 ε = + [ p Y = (b) Using B ELEC2 munication th probabili robabilities hat a 1 is ob ote the input ] 0 = 0 0 X = = ) 1 0 4 ε + + rly, we have ] 1 = 1 0 X = = ( ) 1 1 4 ε + ] [ 2 1 p Y = Bayes’ Rule 210 Spring channel is s ity 1/2, 1/4, of the outpu served as an t and Y den [ ] 0 p X = + 1 1 1 4 2 4 ε = e [ ] 0 p X = + 1 1 1 0 4 4 4 = + ] [ 0 Y p Y = e g 2011 Ho shown in Fi and 1/4, re ut symbols. n output. W Fig. note the outp 0 p Y X = ε 1 p Y X = ε ] 1 1 Y = = omework 2 ig. 1. Suppo spectively. (9) What is the p 1. put [ 1 p X = = [ 1 p X = = 1 1 2 4 ε 2 Solution ose that the probability t ] 1 p Y + = ] 1 p Y + = 1 1 4 4 ε + = n input symb that the inpu 0 2 X = 1 2 X p = 1 4 ols 0, 1, ut was 0? [ ] 2 p X = [ ] 2 X =

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