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![For two random variables X and Y, we have
Var(X) = 8, Var(Y) = 4, Cov(X, Y) = -2.
Find the values of the following quantities. Please show your work.
(a) Cov(Y, X)
(Hint: by using the definition Cov(X, Y) = E[(X – EX)(Y – EY)], observe that
Cov(X, Y) = Cov(Y, X). ]
(b) Cov(X, X)
(Hint: by using the definition of covariance and variance, observe that
Cov(X, X) = Var(X). )
(c) Var(X + Y)
(Hint: use the identity Var(X + Y) =
(d) Var(X + X)
Var(X)+ Var(Y) + 2Cov(X, Y). )
(e) Cov(X, -X)
(Hint: use the identity Cov(aX, bY) = ab · Cov(X,Y). )](https://content.bartleby.com/qna-images/question/a886a924-cb38-4340-a3cf-fc349265e315/bd33cc52-b95e-480e-a2fa-3859ca43b486/kg2y3xb_processed.png)
