09 10 2019 Basic 2.pdf - Probability Statistics Conditional Probabilities Probability Statistics Basic Probability 2 Independence Counting TRAN Hoang

09 10 2019 Basic 2.pdf - Probability Statistics Conditional...

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Probability & Statistics Conditional Probabili- ties Independence Counting 1/18 Probability & Statistics Basic Probability 2 TRAN Hoang Tung NGUYEN Minh Huong NGUYEN Mai Chung University of Science and Technology of Hanoi (USTH) September 10, 2019
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Probability & Statistics Conditional Probabili- ties Independence Counting 2/18 The Course So Far What we have learnt?
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Probability & Statistics Conditional Probabili- ties Independence Counting 2/18 The Course So Far What we have learnt? Probability model: sample space, axioms
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Probability & Statistics Conditional Probabili- ties Independence Counting 2/18 The Course So Far What we have learnt? Probability model: sample space, axioms Notations are very important!
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Probability & Statistics Conditional Probabili- ties Independence Counting 2/18 The Course So Far What we have learnt? Probability model: sample space, axioms Notations are very important! Today
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Probability & Statistics Conditional Probabili- ties Independence Counting 2/18 The Course So Far What we have learnt? Probability model: sample space, axioms Notations are very important! Today Conditional probability, total probability theorem, Bayes’ rule
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Probability & Statistics Conditional Probabili- ties Independence Counting 2/18 The Course So Far What we have learnt? Probability model: sample space, axioms Notations are very important! Today Conditional probability, total probability theorem, Bayes’ rule Independence, conditional independence
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Probability & Statistics Conditional Probabili- ties Independence Counting 2/18 The Course So Far What we have learnt? Probability model: sample space, axioms Notations are very important! Today Conditional probability, total probability theorem, Bayes’ rule Independence, conditional independence Counting
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Probability & Statistics Conditional Probabili- ties Independence Counting 3/18 1 Conditional Probabilities Definition Total Probability Theorem Bayes’ Rule 2 Independence Definition Conditional Independence 3 Counting Counting Principle Combinations
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Probability & Statistics Conditional Probabili- ties Definition Total Probability Theorem Bayes’ Rule Independence Counting 4/18 1 Conditional Probabilities Definition Total Probability Theorem Bayes’ Rule 2 Independence 3 Counting
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Probability & Statistics Conditional Probabili- ties Definition Total Probability Theorem Bayes’ Rule Independence Counting 5/18 Introduction Consider 2 experiments:
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Probability & Statistics Conditional Probabili- ties Definition Total Probability Theorem Bayes’ Rule Independence Counting 5/18 Introduction Consider 2 experiments: Roll a fair 6-sided die Sample space Ω = Probability P (1) = P (2) =
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Probability & Statistics Conditional Probabili- ties Definition Total Probability Theorem Bayes’ Rule Independence Counting 5/18 Introduction Consider 2 experiments: Roll a fair 6-sided die Sample space Ω = { 1 , 2 , 3 , 4 , 5 , 6 } Probability P (1) = 1 / 6 P (2) = 1 / 6
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Probability & Statistics Conditional Probabili- ties Definition Total Probability Theorem Bayes’ Rule Independence Counting 5/18 Introduction Consider 2 experiments: Roll a fair 6-sided die Sample space Ω = { 1 , 2 , 3 , 4 , 5 , 6 }
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