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Unformatted text preview: Principles of Statistics 1 Lecture 4: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 05, 2011 Principles of Statistics 1 Lecture 4: Math 203 – p. 1/ ? ? Bayes Theorem Sometimes we know the conditional probability P ( A  B ) and would like to know about the conditional probability P ( B  A ) , or vice versa. Principles of Statistics 1 Lecture 4: Math 203 – p. 2/ ? ? Bayes Theorem Sometimes we know the conditional probability P ( A  B ) and would like to know about the conditional probability P ( B  A ) , or vice versa. Bayes theorem helps us in these situations. Principles of Statistics 1 Lecture 4: Math 203 – p. 2/ ? ? Bayes Theorem Sometimes we know the conditional probability P ( A  B ) and would like to know about the conditional probability P ( B  A ) , or vice versa. Bayes theorem helps us in these situations. Consider the medical example discussed before. Principles of Statistics 1 Lecture 4: Math 203 – p. 2/ ? ? Bayes Theorem Sometimes we know the conditional probability P ( A  B ) and would like to know about the conditional probability P ( B  A ) , or vice versa. Bayes theorem helps us in these situations. Consider the medical example discussed before. Given that the test result for a person is “+”, what is the probability that the person is actually a carrier? Principles of Statistics 1 Lecture 4: Math 203 – p. 2/ ? ? Bayes Theorem Sometimes we know the conditional probability P ( A  B ) and would like to know about the conditional probability P ( B  A ) , or vice versa. Bayes theorem helps us in these situations. Consider the medical example discussed before. Given that the test result for a person is “+”, what is the probability that the person is actually a carrier? We want: P ( C  +) Principles of Statistics 1 Lecture 4: Math 203 – p. 2/ ? ? Bayes Theorem Sometimes we know the conditional probability P ( A  B ) and would like to know about the conditional probability P ( B  A ) , or vice versa. Bayes theorem helps us in these situations. Consider the medical example discussed before. Given that the test result for a person is “+”, what is the probability that the person is actually a carrier? We want: P ( C  +) Note that in the example we are given P (+  C ) = . 99 . Principles of Statistics 1 Lecture 4: Math 203 – p. 2/ ? ? Bayes theorem in this example says: P ( C  +) = P (+  C ) × P ( C ) P (+  C ) × P ( C ) + P (+  C c ) × P ( C c ) = . 99 × . 07 . 99 × . 07 + . 025 × . 93 = . 0693 . 09255 ≈ . 749 Principles of Statistics 1 Lecture 4: Math 203 – p. 3/ ? ? Bayes theorem in this example says: P ( C  +) = P (+  C ) × P ( C ) P (+  C ) × P ( C ) + P (+  C c ) × P ( C c ) = . 99 × . 07 . 99 × . 07 + . 025 × . 93 = . 0693 . 09255 ≈ . 749 Notice how different the two probabilities P (+  C ) and P ( C  +) are in this example....
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 Summer '08
 Dr.JoseCorrea
 Math, Statistics, Conditional Probability, Probability

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