Day 015_Part_1

Day 015_Part_1 - it is the ace of hearts? what is the...

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Conditional Probability 2/8/2012 1 the conditional probability P ( x | y ) = P ( X=x | Y=y ) is the probability of P ( X=x ) if Y=y is known to be true “conditional probability of x given y Y X X Y True

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Conditional Probability 2/8/2012 2 ? ) | ( ? ) | ( ? ) | ( 3 . 0 ) ( 2 1 3 = = = B A P B A P B A P A P
Conditional Probability 2/8/2012 3 “information changes probabilities” example: roll a fair die; what is the probability that the number is a 3? what is the probability that the number is a 3 if someone tells you that the number is odd? is even? example: pick a playing card from a standard deck; what is the probability that

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Unformatted text preview: it is the ace of hearts? what is the probability that it is the ace of hearts if someone tells you that it is an ace? that is a heart? that it is a king? Conditional Probability 2/8/2012 4 if X and Y are independent then ) ( ) , ( ) | ( y P y x P y x P = ) ( ) ( ) , ( y P x P y x P = ) ( ) ( ) ( ) ( ) | ( x P y P y P x P y x P = = 5 Bayes Formula evidence prior likelihood ) ( ) ( ) | ( ) ( ) ( ) | ( ) ( ) | ( ) , ( = = = = y P x P x y P y x P x P x y P y P y x P y x P posterior...
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This note was uploaded on 02/13/2012 for the course CSE 4421 taught by Professor Burton during the Winter '11 term at York University.

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Day 015_Part_1 - it is the ace of hearts? what is the...

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