Homework Answers
Answer:
Given that:
Suppose the random variables X,Y and Z are related through the model
Y = 2 + 2X + Z,
where Z has mean 0 and variance σZ2 = 16 and X has variance σX2 = 9. Assume X and Z are independent, the find the covariance of X and Y and that of Y and Z. (Hint: write Cov(X,Y ) = Cov(X,2 + 2X + Z)
Cov(X,Y) = Cov(X,2+2X+Z)
Cov(X,Y) = Cov(X,2) + 2*Cov(X,X) + Cov(X,Z)
Cov(X,Y) = 0 + 2*9+0
Cov(X,Y) = 18
(Cov (X,X) = Var(X) ; Covariance of two independent variables is zero. So Cov(X,Z) = 0)
Cov(Z,Y) = Cov(Z,2+2X+Z)
Cov(Z,Y) = Cov(Z,2) + 2*Cov(Z,X) + Cov(Z,Z)
Cov(Z,Y) = 0 + 2*0+16
Cov(Z,Y) = 16
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Suppose the random variables X, Y and Z are related through the
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and Y and that of Y and Z. Hint: write Cov(X, Y ) = Cov(X, 2+2X+Z)
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