(a) Show that for random variables X and Y and constants a, b, c, d,
Cov(ay + bX, cY + dX) = acVar Y + (be + ad)Cov(X, Y) + bdVar X.
(b) Use the result in part (a) to verify that in the structural relationship model with

Cov((βλi + Xi, Yi - βXi) = 0,
the identity on which the Creasy-Williams confidence set is based,
(c) Use the results of part (b) to show that

for any value of β, where rλ(β) is given in (12.2.23). Also, show that the confidence set defined in (12.2.24) has constant coverage probability equal to 1 - α.

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~tn-2