Question: (a) Show that the two quadratic forms s2 = u PXu/(n k) and that given in (7.30) are independent. Hint: Two positive semi-definite

(a) Show that the two quadratic forms s2 = u ¯ PXu/(n − k) and that given in (7.30) are independent.

Hint: Two positive semi-definite quadratic forms uAu and uBu are independent if and only if AB = 0, see Graybill (1961) Theorem 4.10.

(b) Conclude that (7.31) is distributed as an F(g, n − k).

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