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 ).

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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        ).

pagellera10 · Accepted Answer

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        )

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))

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