09 17 2019 Discrete 2.pdf - Probability Statistics Conditional PMF on an Event Multiple Discrete Random Variables Conditional PMF on a Random Variable

09 17 2019 Discrete 2.pdf - Probability Statistics...

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Probability & Statistics Conditional PMF on an Event Multiple Discrete Random Variables Conditional PMF on a Random Variable 1/27 Probability & Statistics Discrete Random Variables 2 TRAN Hoang Tung NGUYEN Minh Huong NGUYEN Mai Chung University of Science and Technology of Hanoi (USTH) September 17, 2019
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Probability & Statistics Conditional PMF on an Event Multiple Discrete Random Variables Conditional PMF on a Random Variable 2/27 The Course So Far What we have learnt?
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Probability & Statistics Conditional PMF on an Event Multiple Discrete Random Variables Conditional PMF on a Random Variable 2/27 The Course So Far What we have learnt? Fundamental probability
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Probability & Statistics Conditional PMF on an Event Multiple Discrete Random Variables Conditional PMF on a Random Variable 2/27 The Course So Far What we have learnt? Fundamental probability Discrete random variable, PMF
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Probability & Statistics Conditional PMF on an Event Multiple Discrete Random Variables Conditional PMF on a Random Variable 2/27 The Course So Far What we have learnt? Fundamental probability Discrete random variable, PMF Expectation: mean, variance, standard deviation
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Probability & Statistics Conditional PMF on an Event Multiple Discrete Random Variables Conditional PMF on a Random Variable 3/27 1 Conditional PMF on an Event Conditional PMF Conditional Expectations Total Expectation Theorem 2 Multiple Discrete Random Variables Joint PMF Marginal PMF Expectation 3 Conditional PMF on a Random Variable Conditional PMF Conditional Expectations Independence
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Probability & Statistics Conditional PMF on an Event Conditional PMF Conditional Expectations Total Expectation Theorem Multiple Discrete Random Variables Conditional PMF on a Random Variable 4/27 1 Conditional PMF on an Event Conditional PMF Conditional Expectations Total Expectation Theorem 2 Multiple Discrete Random Variables 3 Conditional PMF on a Random Variable
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Probability & Statistics Conditional PMF on an Event Conditional PMF Conditional Expectations Total Expectation Theorem Multiple Discrete Random Variables Conditional PMF on a Random Variable 5/27 Conditional PMF on an Event Conditional PMF The conditional PMF of X , given an event A with P ( A ) > 0 , is defined by p X | A ( x ) , P ( X = x | A ) , P ( { X = x } ∩ A ) P ( A )
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Probability & Statistics Conditional PMF on an Event Conditional PMF Conditional Expectations Total Expectation Theorem Multiple Discrete Random Variables Conditional PMF on a Random Variable 5/27 Conditional PMF on an Event Conditional PMF The conditional PMF of X , given an event A with P ( A ) > 0 , is defined by p X | A ( x ) , P ( X = x | A ) , P ( { X = x } ∩ A ) P ( A ) Sanity check: verify that X x p X | A ( x ) = 1
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Probability & Statistics Conditional PMF on an Event Conditional PMF Conditional Expectations Total Expectation Theorem Multiple Discrete Random Variables Conditional PMF on a Random Variable 6/27 Conditional PMF on an Event Example Let X be the roll of a fair six-sided die A be the event that the roll is an even number Calculate p X | A ( x ) .
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Probability & Statistics Conditional PMF on an Event Conditional PMF Conditional
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