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[XYZ].

cuuhorre76

cuuhorre76

Answered question

2022-09-10

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[XYZ].

Answer & Explanation

Aldo Harrington

Aldo Harrington

Beginner2022-09-11Added 12 answers

Given:
( 1 , 2 , 3 ) = p ( 2 , 1 , 1 ) = p ( 2 , 2 , 1 ) = p ( 2 , 3 , 2 ) = 1 4
The expected value (or mean) is the sum of the product of each possibility with its probability :
E ( X Y Z ) = x y z p ( x , y , z )
= 1 2 3 1 4 + 2 1 1 1 4
+ 2 2 1 1 4 + 2 3 2 1 4
= 6 4 + 2 4 + 4 4 + 12 4
= 6 + 2 + 4 + 12 4
= 24 4
=6

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