Conditional Probability, Total Probability Theorem and ... - Berlin Chen

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Using Conditional Probability for Modeling (2/2)PA BP A BcP A c BcP A BcProbability-Berlin Chen 10
Multiplication (Chain) Rule• Assuming that all of the conditioning events havepositive probability, we haveP nn1 A P A P A A P A A A PA i1i 1 2 1 3 1 2 n i1Ai– The above formula can be verified by writingPnA PAn1i11P A1 A2P A1 A2 A3P iAi1 i 1n PA1 PA1 A2 P i A i– For the case of just two events, the multiplication rule is simplythe definition of conditional probabilityA A APAP P1 2 1 2 A1Probability-Berlin Chen 11
Page 1 and 2: Conditional Probability, Total Prob
Page 3 and 4: Conditional Probability (2/2)• Wh
Page 5 and 6: Conditional Probabilities Satisfy G
Page 7 and 8: Simple Examples using Conditional P
Page 9: Using Conditional Probability for M
Page 13 and 14: Multiplication (Chain) Rule: Exampl
Page 15 and 16: Total Probability Theorem (2/2)Figu
Page 17 and 18: Some Examples Using Total Probabili
Page 19 and 20: Bayes’ Rule• Let A 1, A2,,A n b
Page 21 and 22: Inference Using Bayes’ Rule (2/2)
Page 23: Homework -1• Chapter 1 : Addition

Conditional Probability, Total Probability Theorem and ... - Berlin Chen

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