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3ConditionalProbability-1

3ConditionalProbability-1 - Conditional Probability and...

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Click to edit Master subtitle style  EE 3180 Probability and  Conditional Probability and  Bayes Theorem Jeffrey B. Burl 11

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EE 3180 Probability and  Conditional Probability n Conditional probability is very frequently  used in signal processing. n Probability that an airplane is at a given  distance given a received radar signal. n Probability of alternator failure given a  current output measurement. n Typical to measure something to infer  22
EE 3180 Probability and  Conditional Probability via  Set Theory n The conditional probability of A given B is defined: n Note that if A and B are elementary events: n But A and B do not have to be elementary events. 33 Pr( ) Pr( | ) , Pr( ) 0 Pr( ) A B A B B B B = Pr( ) Pr( , ) A B A B =

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EE 3180 Probability and  Example n Consider the case of flipping 4 coins.  n Define A as having the number of heads be 2 or fewer. n Define B as having an even number of heads. n Note that the point probability for this experiment  would consist of the probabilities of each combination  of four coins. n The conditional probability of A given B is: 44 Pr( ) 7 /16 7 Pr( | ) Pr( ) 1/ 2 8 A B A B B B = = =
EE 3180 Probability and  Properties of Conditional

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