st371-17 joint rv 01

st371-17 joint rv 01 - ST371 Introduction to Probability...

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(c) Tom Gerig ST371-17 joint rv 01 Page 1 ST371 Introduction to Probability and Distribution Theory Joint Probability Distributions Discrete Random Variables
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(c) Tom Gerig ST371-17 joint rv 01 Page 2 Outline Discrete random variables: Joint of ( , ) Marginal distribution ( ) of Conditional distribution of given Independence of two 's pmf X Y pmf X X Y y rv
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(c) Tom Gerig ST371-17 joint rv 01 Page 3 ( , ) ( ) p x y P X x and Y y joint pr Let ( , oba ) be two bility ma discrete 's. Th ss funct eir is de io fi : n ned as X Y rv and is defined over the range of ( , ) XY If is any subset of the range of ( , ), then A X Y ( , ) (( , ) ) ( , ) x y A P X Y A p x y  Joint Distribution of Two Discrete Random Variable
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(c) Tom Gerig ST371-17 joint rv 01 Page 4 The joint probability mass function ( ) must satisfy: jpmf ( , ) 0, for all values of ( , ) p x y x y  ( , ) ( , ) 1 range of X Y p x y   Joint Distribution of Two Discrete Random Variable
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(c) Tom Gerig ST371-17 joint rv 01 Page 5 Suppose that the for ( , ) is: jpmf X Y ( , ) 0 1 2 1 0.3 0.2 0.1 2 0.1 0.1 0.2 y p x y x Joint Distribution - Example Range of ( , ): XY (1,1), (1,2), (1,3), (2,1), (2,2), (2,3)
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(c) Tom Gerig ST371-17 joint rv 01 Page 6 ( , ) 0 1 2 1 0.3 0.2 0.1 2 0.1 0.1 0.2 y p x y x Joint Distribution - Example 23 11 ( , ) 1 xy P x y  
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st371-17 joint rv 01 - ST371 Introduction to Probability...

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