Lecture_4-2_July_2010

Lecture_4-2_July_2010 - EE 131A Probability Professor Kung...

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UCLA EE131A (KY) 1 EE 131A Probability Professor Kung Yao Electrical Engineering Department University of California, Los Angeles M.S. On-Line Engineering Program Lecture 4-2
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UCLA EE131A (KY) 2 Conditional Probability is a Probability P( A | B ) satisfies all the axioms of probability. Axiom I. 0 P( A | B ) . Axiom II. P( S | B ) = 1 . Axiom III’. If A 1 , A 2 , …, are mutually exclusive (or disjoint) (i.e., A i A j = , for all i and j), then  ii i=1 i=1 PP . ||    AB
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UCLA EE131A (KY) 3 Conditional Probability (1) Ex. 1. Binary Symmetric Channel ( BSC ) Consider the simplest model for a binary digital communication channel for transmitting an input of either an “0” or an “1.” Denote A 0 for a channel input of an “0” and A 1 for an input of an “1.” The output can be either an “0” or an “1.” Denote B 0 for a channel output of an “0” and B 1 for an output of “1.” Since the channel is imperfect (i.e., due to noise and other disturbance), sending any A i , i = 0, 1, can result in any B j , j = 0, 1.
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UCLA EE131A (KY) 4 Conditional Probability (2) Let the probability of receiving B 0 given A 1 was sent, be denoted by the conditional probability P(B 0 |A 1 ) = , ( ~ small) (1) Probability of receiving B 1 given A 1 was sent becomes P(B 1 |A 1 ) = P(B 0 C |A 1 ) = 1 - .( 2 ) Channel is symmetric if prob. of receiving B 1 given A 0 P(B 1 |A 0 ) = 3 ) Then the probability of receiving B 0
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This note was uploaded on 11/05/2010 for the course ELECTRICAL EE131A taught by Professor Kungyao during the Spring '10 term at UCLA.

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Lecture_4-2_July_2010 - EE 131A Probability Professor Kung...

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