=+29.10. Let X„, = (X .. ], . . ., X„ .. ), n = 1,2 ,..., be random vectors satisfying the mixing condition (27.19) with @ ,, = O(n ). Suppose that the sequence is stationary

(the distribution of (X ,.,..., X ,, ,, ) is the same for all n), that E[ X ... ] =0, and that the Xmu are uniformly bounded. Show that if S, = X, + . . . +X ,, then S„/ vn has in the limit the centered normal distribution with covariances 8

E[X]„X]]+ [ E[X]X ,.,.. ] + [E[ X1.X]

Hint: Use the Cramér-Wold device.