5.96 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)

, respectively, Use the basic definition of the covariance of two-random variables to\ establish that\ a

Cov(Y_(1),Y_(2))=Cov(Y_(2),Y_(1))

.\ b

Cov(Y_(1),Y_(1))=V(Y_(1))=\\\\sigma _(1)^(2)

. That is, the covariance of a random variable and itself is just.\ the variance of the random variable.

6 Suppose that the random suriables Y1 and Y2 have means 1 and 2 and variances 12 and 22, respectively. Use the basic detinition of the covariance of two random variables to establish that a Cov(Y1,Y2)=Cov(Y2,Y1) b Cov(Y1,Y1)=V(Y1)=12. That is, the covariance of a random variable and itself is just the variance of the random variable