Suppose that the random variables Y_(1) and Y_(2) have means mu_(1) and mu_(2) and variances sigma_(1)^(2) and sigma_(2)^(2), rrespectively. Use the basic definition of the covariance of two random variables to establish that Cov(Y_(1), Y_(2))=Cov(Y_(2), Y_(1))

Seamus Mcknight

Seamus Mcknight

Answered question

2022-09-22

Suppose that the random variables Y 1 and Y 2 have means μ 1 and μ 2 and variances σ 1 2 and σ 2 2 , respectively. Use the basic definition of the covariance of two random variables to establish that C o v ( Y 1 , Y 2 ) = C o v ( Y 2 , Y 1 ).

Answer & Explanation

pagellera10

pagellera10

Beginner2022-09-23Added 7 answers

Theorem:
C o v ( Y 1 , Y 2 ) = E ( Y 1 Y 2 ) E ( Y 1 ) E ( Y 2 )
Then we obtain:
C o v ( Y 1 , Y 2 ) = E ( Y 1 Y 2 ) E ( Y 1 ) E ( Y 2 ) = E ( Y 2 Y 1 ) E ( Y 2 ) E ( Y 1 ) = C o v ( Y 2 , Y 1 )
Result:
C o v ( Y 1 , Y 2 ) = C o v ( Y 2 , Y 1 )

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