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COnDITIONAL Probability

COnDITIONAL Probability. Onur DOĞAN. The Definition of Conditional Probability.

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COnDITIONAL Probability

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  1. COnDITIONALProbability Onur DOĞAN

  2. The Definition of Conditional Probability A major use of probability in statistical inference is the updating of probabilitieswhen certain events are observed. The updated probability of event A after welearn that event B has occurred is the conditional probability of A given B.

  3. The Definition of Conditional Probability

  4. Example 1

  5. Example 2

  6. The Multiplication Rule for Conditional Probabilities

  7. Example

  8. MultiplicationRuleforConditionalProbabilities.

  9. MultiplicationRuleforConditionalProbabilities.

  10. Law of Total Probability

  11. Example

  12. IndependentEvents If learning that B has occurred does not change the probability of A, then we saythat A and B are independent. There are many cases in which events A and Bare not independent, but they would be independent if we learned that some otherevent C had occurred. In this case, A and B are conditionally independent given C.

  13. Independence of SeveralEvents

  14. Independence of SeveralEvents

  15. Bayes’ Theorem Suppose that we are interested in which of several disjoint events B1, . . . , Bk willoccur and that we will get to observe some other event A. If Pr(A|Bi) is availablefor each i, then Bayes’ theorem is a useful formula for computing the conditionalprobabilities of the Bi events given A.

  16. Bayes’ Theorem

  17. Example

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