10.7. (Sec. 10.6) Let x\"), ... , x}J') be observations from N( .... (·). I.), I' = 1.2. and let A.= Dx~·) -i(v»)(x~:) -i(·»)'.

(a) Prove that the likelihood ratio test for H::II =:I2 is equivalent to rejecting H if

(b) Let dr, d~, .. . , d; be the roots of l:I j - A:I21 = 0, and let

Show that T is distributed as IB,I·IB21/IB, +B212. where B, is dis·
tributed according to WeD". N - 1) and B2 is distributed according to W(J,N- 1). Show that T is distributed as IDC,DI'IC21/IDCID+C212, where C, is distributed according to W(l, N - 1).

442 T= 14, +421 C.