st371-19 joint rv 03

st371-19 joint rv 03 - ST371 Introduction to Probability...

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(c) Tom Gerig ST371-19 joint rv 03 Page 1 ST371 Introduction to Probability and Distribution Theory Covariance and Correlation Joint Probability Distributions:
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(c) Tom Gerig ST371-19 joint rv 03 Page 2 Expectation of a Function of ( , ) XY Let ( , ) be discrete random variables with joint probability mass function ( , ) and let let be any function of ( , ). Then p x y h X Y ( , ) ( ( , )) ( , ) ( , ) range of X Y E h X Y h x y p x y
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(c) Tom Gerig ST371-19 joint rv 03 Page 3 The following is the joint for ( , ): pmf X Y Example Let ( , ) , then h X Y XY 22 10 [ ( , )] ( , ) xy E h X Y xy p x y    1 0 0.3 1 1 0.2 1 2 0.1          2 0 0.1 2 1 0.2 2 2 0.1 1.2          ( , ) 0 1 2 1 0.3 0.2 0.1 2 0.1 0.2 0.1 y p x y x
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(c) Tom Gerig ST371-19 joint rv 03 Page 4 The following is the joint for ( , ): pmf X Y Let ( , ) ( , ), then h X Y MAX X Y 22 10 [ ( , )] ( , ) ( , ) xy E h X Y MAX x y p x y    1 0.3 1 0.2 2 0.1       2 0.1 2 0.2 2 0.1 1.5       Example ( , ) 0 1 2 1 0.3 0.2 0.1 2 0.1 0.2 0.1 y p x y x
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(c) Tom Gerig ST371-19 joint rv 03 Page 5
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st371-19 joint rv 03 - ST371 Introduction to Probability...

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