EE131A TA Recitation 2

EE131A TA Recitation 2 - EE131A Probability TA Recitation 2...

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EE131A Probability TA Recitation 2 Chihkai Chen chihkai@ucla.edu Office hours: Monday, 9:15-10:15pm Tuesday, 9:15-10:15pm
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Bayes Rule j j jj n k k=1 n kk k=1 P( ) = P( ) | Def. of cond. prob. P( ) P( | )P( ) Def. of cond. prob. = Th. of total prob. P( ) P( | )P( ) Nothing new = Def P( | )P( ) AB B Α Β BA A A A I I . of cond. prob.
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jj j n kk k=1 P( | )P( ) Bayes' Rule: P( | ) = P( | )P( ) BA A AB A • Ex. Binary Symmetric Channel (BSC) A i B j ε 1- ε 1- ε ε 0 1 1 0 BSC Equal prior prob.P( A 0 ) = P( A 1 ) = ½. P( B 1 | A 0 ) = ε ; P( B 0 | A 0 ) = 1- ε . P( B 0 | A 1 ) = ε ; P( B 1 | A 1 ) = 1- ε . Received B 1 , what it the most probable A i ?
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== 1 Assume we receive B P( | )P( ) P( | )P( ) 10 0 0 P( | ) = = 01 1 P( | )P( ) + P( | )P( ) 0 11 1 P( | )P( ) 1k k k=0 ε 1/2 ε /2 ε 1/2+(1- ε )*1/2 1/2 = ε . P( | )P( ) 1 P( | ) = P( | 1 BA A A AB A A A A B P( | )P( ) 1 = 1 P( | )P( ) + P( | )P( ) 0 1 )P( ) kk k=0 (1- ε )*1/2 (1- ε )/2 ε 1/2+(1- ε )*1/2 1/2 = (1- ε ). A A A AA jj j n k=1 P( | )P( ) Bayes' Rule:
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EE131A TA Recitation 2 - EE131A Probability TA Recitation 2...

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