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 wi Find the pr Suppose th 1? 2? (12) Solution: Let X deno (a) [ pY p Y = ( 1 1 2 = Similar [ p Y = 1 2 ε = + [ p Y = (b) Using B ELEC2 munication th probabili robabilities hat a 1 is ob ote the input ] 0 = 00 X == ) 1 0 4 − +⋅ + rly, we have ] 1 = 10 X () 1 1 4 −+ ][ 21 p Y =− Bayes’ Rule 210 Sprin channel is s ity 1/2, 1/4, of the outpu served as an t and Y den [ ] 0 pX = + 11 1 42 4 [ ] 0 =+ 1 0 44 4 ⋅=+ 0 Y p Y g 2011 Ho shown in Fi and 1/4, re ut symbols. n output. W Fig. note the outp 0 X = 1 X = ] Y ==− omework 2 ig. 1. Suppo spectively. (9) hat is the p 1. put [ 1 = [ 1 = = 24 −− ⎟⎜ 2 Solution ose that the probability t ] 1 = + = ] 1 += input symb that the inpu 02 X = 12 Xp = = 1 4 ols 0, 1, ut was 0? [ ] 2 p X = [ ] 2 X =
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[] 1 10 0 2 2 01 11 44 pY X pX Y ε ⎡⎤ == = ⎣⎦ = = = = + + () 1 1 1 1 4 X Y = = = = = + + [ ] 21 1 0 0 1 X Y = = = = = + 2. Suppose that a bus arrives at a bus stop at a time that is chosen at random in the interval 7:00 to 7:15. When the bus arrives at the bus stop, and it departs immediately, i.e., it does not wait at the bus stop. (a) What is the probability that the bus arrives between 7:05:00 and 7:05:30? (3) (b) What is the conditional probability that the bus will arrive in the next 30 seconds if you arrive at the bus stop at 7:05:00 and the bus has not arrived yet? (4)
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This note was uploaded on 10/16/2011 for the course ELEC 308,315,10 taught by Professor Prof.shenghuisong during the Spring '11 term at CUHK.

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HW2_Spring11_sol - ELEC210 Spring 2011 Homework 2 Solution...

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