The joint probability mass function of the random variables X, Y, Z is p (1,2,3)=p(2,1,1)=p(2,2,1)=p(2,3,2)=1/4 Find E[XY+XZ+YZ].

Quinlan7g 2022-09-25 Answered
The joint probability mass function of the random variables X, Y, Z is p ( 1 , 2 , 3 ) = p ( 2 , 1 , 1 ) = p ( 2 , 2 , 1 ) = p ( 2 , 3 , 2 ) = 1 4 Find E[XY+XZ+YZ].
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Answers (1)

Haylee Krause
Answered 2022-09-26 Author has 10 answers
The expected value (or mean) is the sum of the product of each possibility with its probability:
E ( X Y + X Z + Y Z ) = ( x y + x z + y z ) p ( x , y , z )
= ( 1 ( 2 ) + 1 ( 3 ) + 2 ( 3 ) ) 1 4 + ( 2 ( 1 ) + 2 ( 1 ) + 1 ( 1 ) ) 1 4
= ( 2 ( 2 ) + 2 ( 1 ) + 2 ( 1 ) ) 1 4 + ( 2 ( 3 ) + 2 ( 2 ) + 3 ( 2 ) ) 1 4
= 11 4 + 5 4 + 8 4 + 16 4
= 11 + 5 + 8 + 16 4
= 40 4
=10
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