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Unformatted text preview: 1 Fourth Problem Assignment EECS 401 Problem 1 Joe and Helen each know that the a priori probability that her mother will be home on any given night is 0.6. However, Helen can determine her mothers plan for the night at 6 P.M., and then, at 6:15 P.M., she has her only chance of the evening to shout one of two code words across the river to Joe. He will visit her with probability 1.0 if he thinks Helens message means Ma will be away, and he will stay home with probability 1.0 if he thinks the message means Ma will be home. But Helen has a meek voice and the river is channeled for heavy barge traffic. Thus she is faced with the problem of coding for a noisy channel. She has decided to use a code containing only the code words A and B . The channel is described by P ( a | A ) = 2 3 , P ( a | B ) = 1 4 , P ( b | A ) = 1 3 , P ( b | B ) = 3 4 where a is the event that Joe thinks message is A and b is the event that Joe thinks message is B . (a) In order to minimize the probability of error between transmitted and received messages, should Helen and Joe agree to use code I or code II? Code I Code II A = Ma away A = Ma home B = Ma home B = Ma away (b) Helen and Joe put the following cash values (in dollars) on all possible outcomes of a day Ma home and Joe comes-30 Ma home and Joe doesnt come Ma away and Joe comes +30 Ma away and Joe doesnt come-5...
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This note was uploaded on 04/04/2012 for the course ECE 139 taught by Professor Staff during the Spring '08 term at UCSB.
- Spring '08