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Given the random variables X1 X2 and X3 having the

Given the random variables X1, X2, and X3 having the joint density f(x1, x2, x3), show that if the regression of X3 on X1 and X2 is linear and written as

Then

Where µi = E(Xi), σ2i = var(Xi), and σij = cov(Xi,Xj). [Proceed as on pages 386 and 387, multiplying by (x1 – µ1) and (x2 – µ2), respectively, to obtain the second and third equations.]

Then

Where µi = E(Xi), σ2i = var(Xi), and σij = cov(Xi,Xj). [Proceed as on pages 386 and 387, multiplying by (x1 – µ1) and (x2 – µ2), respectively, to obtain the second and third equations.]

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